Solutions Manual: Part IV Market Power Summary answers to the By yourself questions

Transcription

1 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 Solutions Manual: Part IV Market Power Summary answers to the y yoursel questions

2 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 Chapter 5 X5. Suppose that we are onsidering the monopoly enjoyed y the only akery on an island. Disuss its deision making proess, explaining why we onsider that it will e a prie maker, rather than a prie taker. We deine the market or read on this island. s the only akery, the irm s supply is also the market supply. I we imagine the akery as ixing the amount o read that it will sell, the market prie will emerge as the prie at whih that quantity an e sold. More generally, we expet the akery to hoose the output at whih it maximizes proit given market learing. X5. Suppose that a monopoly aes inverse demand, p = p(q ) = p p q and total osts, C = q. a) Otain the irm s marginal and average osts, MC and C, and its total, marginal and average revenues, TR, MR, and R. dc Marginal ost, MC :MC. verage ost, C : C. dq Total revenue, TR = p.q = (p p q )q ; so marginal revenue, MR and average revenue, R : R R q p p q. C q dtr dq :MR p p q ; ) Calulate the proit-maximizing level o output, the prie that the irm will then harge, and the proits that it will make. First-order ondition or proit maximization is that marginal revenue equals marginal ost. (We do not hek the seond-order ondition, that the derivative o marginal ost with respet to output is greater than the derivative o marginal revenue with respet to output at the proit maximizing output.) Here, p p q =, so rearranging, p q = p, and we otain proit maximizing output q * p p. Sustituting into the expression or inverse demand, p p * p p p p p p p p 4p ; and so we otain proit (q *) = (p * - )q * =. ) Sketh a diagram showing MC, C, MR, and R. Indiate learly the proit-maximizing output, and the resulting prie and proits. In a diagram with output q shown on the horizontal axis and measures o ost and revenue shown on the vertial axis, the average ost and marginal ost are oinident, a horizontal line with equation MC = C =. The average revenue (or inverse demand) urve is a downward sloping line, passing through the vertial axis at (, p ), and with gradient p. The marginal revenue urve is also a downward sloping line, passing through (, p ), ut with gradient -p, it is twie as steep as the average revenue urve. The proit maximizing output is where the marginal ost urve uts through the marginal revenue urve. We see that the average ost is then greater than the average revenue, ensuring that the irm is ale to make proits, shown y a retangle ormed y the vertial axis, the average ost urve, a vertial line passing through the point where MC = MR, and losed y a horizontal line at height R(p *) = ½(p + ). X5.3 Repeat X5. or the inverse demand p = p p q and the total osts C = + q + q. Marginal ost, MC :MC dc C dq q. verage ost, C : C q q q.

3 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 Total revenue, TR = p.q = (p p q )q ; so marginal revenue, MR and average revenue, R : R R q p p q. dtr dq :MR p p q ; First-order ondition or proit maximization is that marginal revenue equals marginal ost. (We do not hek the seond-order ondition, that the derivative o marginal ost with respet to output is greater than the derivative o marginal revenue with respet to output at the proit maximizing output.) Here, p p q = + q, so rearranging, (p + )q = p, and we otain proit p maximizing output q * p. Sustituting into the expression or inverse demand, p p p p p * p p p p ; and we otain proit (q *) = -(p + )q + (p )q = p 4 p p 4p p p. In a diagram with output q shown on the horizontal axis and measures o ost and revenue shown on the vertial axis, the average ost urve never reahes the vertial axis. With ixed osts, the vertial axis orms an asymptote, and the urve is downward sloping. In the same way, as output inreases without limit, average ixed ost alls to zero, and the urve approahes the upward-sloping line VC = + q, whih meets the vertial axis at (, ) and has gradient. The marginal ost urve is a line, also passing through (, ), ut with gradient ; it is thereore twie as steep as the average variale ost urve. We an show that the average ost is minimized at output q =, where average ost equals marginal ost. The average revenue (or inverse demand) urve is a downward sloping line, passing through the vertial axis at (, p ), and with gradient p. The marginal revenue urve is also a downward sloping line, passing through (, p ), ut with gradient -p, it is twie as steep as the average revenue urve. The proit maximizing output is where the marginal ost urve uts through the marginal revenue urve. The presene o ixed osts means that it is possile that the irm will make losses; we deine the irm s total proit as the area o the retangle ounded y the vertial axis, horizontal lines the average revenue at the proit maximizing output, the average ost at the proit maximizing output and a vertial line at the proit maximizing output X5.4 Repeat Exerise X5. or the inverse demand p = q, with these total osts: (a) C = q ; () C = q /3. dc a) Marginal ost, MC :MC. verage ost, C : C. dq Total revenue, TR = p.q = (q - )q = ; so marginal revenue, MR :MR ; and average revenue, R : R R q q Sine marginal revenue is zero, and marginal ost is greater than zero, the irst-order onditions or proit maximization annot e met; ut any inrease in output redues proits. The irm annot do etter than produe zero output, inurring no osts, and making proit () =. s in previous ases, in a diagram with output on the horizontal axis and measures o ost and revenue on the vertial axis, the marginal and average ost urves are horizontal lines. The marginal revenue urve is the horizontal axis; and the average revenue urve is a retangular hyperola, always downward sloping, and with the axes orming asymptotes. dc ) Marginal ost, 3 MC :MC q. verage ost, 3 C : C q. Measures dq o revenue are as noted in part a). 3 C q C q dtr dq

4 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 One again, we have a situation where marginal revenue is less than marginal ost at all levels o output, so that the irm produes zero output to maximize proits. The marginal and average ost urves are downward sloping, urved, and never touh the axes. t every level o output, average ost is 5% greater than marginal ost. X5.5 Repeat Exerise X5. or the inverse demand p = p(q ) = p p q, with these total osts: (a) C = q ; () C = q 3/. We have the same inverse demand as in X5.. So total revenue, TR = p.q = (p p q )q ; and marginal revenue, MR R : R R q p p q. :MR dtr dq p p q ; and average revenue, a) The ost untion is a speial ase o the ost untion in X5.3, and we otain marginal ost, MC :MC dc C dq q. verage ost, C : C q q. The ondition MR = MC is satisied when p p q = q. Rearranging this expression, p we otain q * p. The proit maximizing prie, p* = p p q * = p p, so p p that the total proit, = (p q )q = 4p. In a diagram, we have already desried all o these ost and revenue urves. ll are straight lines. The average revenue urve passes through (, p ), and is downward sloping with gradient p. The marginal revenue urve also passes through (, p ), ut is twie as steep, so has gradient p. The average ost urve and marginal ost urve oth start at the origin; and the marginal ost urve is twie as steep as the average ost urve, with gradients and, respetively. dc 3 ) We otain marginal ost, MC :MC q. verage ost, C : C q. dq 3 The ondition MR = MC is satisied when p p q. We an solve this y using q the quadrati ormula, ut omit this here, instead onentrating on the graphial analysis. The marginal and average revenue urves have the same shape as desried aove. The average ost and marginal ost urves oth start rom the origin, and oth are upward sloping and onave they are arms o two distint paraolas. Marginal ost is everywhere 5% greater than average ost, and marginal revenue is everywhere less than average revenue. We an thereore e sure that where marginal revenue equals marginal ost, the irm makes proits. X5.6 Conirm that in Figure 5.: (a) there is no produer surplus; and () the maximum onsumer surplus is equivalent to the area enlosed y the marginal ost and average revenue urves. For every level o output, q, MC(q) = C(q) =. Deining the rate o hange o produer surplus as the dierene etween marginal and average ost, sine MC(q) C(q) =, the q total surplus when produing output q may e written PS = dq =. In the same way deining the rate o hange o onsumer surplus as the dierene etween average revenue and marginal revenue at any level o output, we deine total onsumer surplus as CS q Rq MRq dq. Now deine q : R(q ) =, whih is to say that we set the irm s output so that the market prie is equal to the irm s marginal ost. Then R(q ) is the irm s WT or every level o output, and q is the maximum output. The onsumer surplus is then inreasing as q inreases towards q. C q

5 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 X5.7 Suppose that the market demand o a monopoly is linear (and dereasing in prie), while the average ost is linear (and inreasing in output). Sketh a diagram to show the average and marginal revenues and the average and marginal osts. Indiate the proit-maximizing and the welare-maximizing levels o output; and lael the areas on your diagram that represent the irm s proits, its produer surplus, the onsumers surplus, and the welare loss rom the monopoly. In a diagram with irm output, q, measured on the horizontal axis, and measures o ost and revenue on the vertial axis, the average and marginal revenue urves are downward sloping straight lines, interseting the vertial axis at the same point, ut with the marginal revenue urve twie as steep as the average revenue urve. In the same way, the average and marginal ost urves are straight lines, interseting the vertial axis at the same point, whih has to e lower than the intersetion o the average and marginal revenue urves with the axis. The average and marginal ost urves are upward sloping, with the marginal ost urve twie as steep as the average ost urve. The irm maximizes proit at output q*, hosen so that MR(q*) = MC(q*). The irm harges prie R(q*) > C(q*), the ost per unit o output, and so there are positive proits. We deine the onsumer surplus as the triangle ounded y the average and marginal revenue urves to the let o output q*; the produer surplus as the triangle ounded y the average and marginal ost urves to the let o output q*; the irm s proits as the triangle ormed y the vertial axis and the marginal revenue and marginal ost urves; and the welare loss as the triangle to the right o output q*, ounded y the average revenue and marginal ost urves. X5.8 Why might it e reasonale to onlude that in Exerises X5. X5.6 we are onsidering the long run? How reasonale is it to expet there to e a monopoly in these irumstanes? In all o these examples, we have exluded ixed osts o prodution, indiating that there are no ixed ators, whih deines the long-run. Monopoly ours when a irm aes no ompetitors. We have noted that in peret ompetition, in the short-run, there is no possiility o irm entry, ut that long-run entry eliminates proits. In monopoly, we exlude entry. Given that the monopoly makes proits, we need to ind some explanation, suh as inreasing returns to sale, or statutory protetion o the monopoly. X5.9 dapt Figure 5.3 to represent the monopoly making short-run deisions. Illustrate two distint ases: () the monopoly makes proits in the short run; and () the monopoly makes losses, ut wishes to ontinue prodution. Moving rom the long-run to the short-run, we show oth the average variale ost urve and the average ost urve. We expet the average variale ost urve to have similar properties to the average ost urve in Figure 5.3; possily U-shaped, ut ertainly eventually inreasing, i not everywhere inreasing, while releting the element o average ixed osts, the average ost urve will e never reah the vertial axis, whih ats as its asymptote. The average ost urve will ertainly have a minimum, and output inreases without limit, it approahes the average variale ost urve. In order or the monopoly to make proits in the short run, the average ost urve lies elow the average revenue urve at the proit-maximizing output (or whih marginal ost equals marginal revenue). For the irm to make a loss, the average ost urve lies aove the average revenue urve at the proit-maximizing output. X5. pplying the same argument to marginal revenue as to marginal osts (in Figure 5.3), interpret the area etween the output axis and the marginal revenue urve. We deine marginal revenue as the rate o hange o revenue as output inreases. The area underneath the marginal revenue urve (etween the vertial axis and the line q = q )

6 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 thereore represents the sum o revenue inrements aross a ontinuum o ininitesimally small inreases in output. It is thereore the total revenue, R(q ). We onlude that R(q ) = q q MR dq. X5. Explain why the area etween the marginal revenue and marginal ost urves yields the irm s proit. Essentially, we uild on the argument already developed. The expression, {MR(q) MC(q)}dq represents the inrease in proit when output inreases y some ininitesimally small amount, rom q to q + dq. The integral q q MRq MC q dq is then the sum o these inreases in proits as output inreases rom q = to q = q. The irm s proit is shown in a diagram as the area ounded y the vertial axis and its output and the marginal revenue and marginal ost urves. We should note here that it is possile that or large enough values o q, MR(q ) < MC(q ), so that inreasing output leads to a redution in proit. X5. Interpret the area in Figure 5.3 etween the inverse demand (average revenue) urve and the marginal ost urve in terms o onsumers WTP and the monopoly s WT. Hene justiy the argument that the area laelled Welare loss represents the ost to soiety o prodution eing undertaken y a monopoly. The inverse demand urve shows the prie that the marginal onsumer is willing to pay, given the irm s urrent output; the marginal ost urve shows the irm s WT, given its output. We know that so long as WTP > WT, there is a surplus rom ompleting at transation, so that we an write the rate o hange o surplus,, with respet to output, q, as the derivative, d R q MC q ; so that the total surplus rom output q may e written dq q q Rq MC q dq. ssume that R(q) > MC(q) or all values o q: q < q M, ut that R(q) < MC(q) or higher values o output. It then ollows that surplus inreases until q < q, and dereases at higher output levels, so that surplus is maximized when q = q M. I the irm hooses to produe output q *: q * < q M, total surplus is less than its maximum value; and we M q deine the welare loss q Rq MC q dq q X5.3 Suppose that it is proposed that the monopolist should e required to produe output Q M, the welare-maximizing output. Write down an expression or the loss inurred y the monopolist in terms o the marginal revenue and ost untions, illustrating this area on a diagram. How might it e possile to ompensate the monopolist or this loss? The monopolist maximizes proits at output q *; required to produe output q M, the M M q monopolist loses the dierene in proits q q * MRq MC q q * dq. Note that this redution in proits is less than the inrease in onsumer surplus; i onsumers agree to ompensate the monopolist or inreasing output, agreeing olletively to transer this amount (olletively and voluntarily) to the produe, on ondition that the produer inreases output, then the produer would e no worse o than eore eing required to inrease output and onsumers (as a group) are etter o. X5.4 Given the marginal revenue and marginal ost urves in eah o these three ases: a) Find the output or whih marginal revenue equals marginal ost. ) Otain the ollowing untions o output: (i) total revenue; (ii) average revenue; (iii) total ost; (iv) proit; and (v) onsumer surplus.

7 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 ) Sketh diagrams showing the marginal and average revenue urves and the marginal ost urve, indiating the total ost o the proit-maximizing output, the irm s proit, and the onsumer surplus. d) Estimate the welare loss rom monopoly: i. MC(q) = +.q; MR(q) = 4; ii. MC(q) = 3; MR(q) = 6.5q; iii. MC(q) = +.3q; MR(q) = 8.9q. i. I MR = MC, then +.q = 4, so q =. We assume no ixed osts. Total revenue R = Rq 4q. verage revenue R: R(q) = q = 4. q Total ost C =.q.dqq.q.q. Proit = q MC q q 4q q 4.dq 4q ; so we write R: R(q) = q.q. We write C: C(q) = q + q. dq.qdqq.q MR. Consumer surplus, CS() = q MRq dq 4 R 4 dq. We illustrate all o this inormation in a diagram with the level o output on the horizontal axis and measures o ost and revenue on the vertial axis. verage and marginal revenues are horizontal lines, R(q) = MR(q) = 4; marginal ost is shown y an upward sloping line, passing through (, ) and with gradient., so that it intersets MR at q * =. This is the proit maximizing output, and we an see the irm s proit (and the produer surplus) as the triangle ormed y the vertial axis and the marginal revenue and marginal ost urves. The total ost o the proit maximizing output is the area elow that triangle, ounded y the line q =. Consumer surplus is here zero. ii. I MR = MC, then 6.5q* = 3, so.5q* = 3; and q =. We assume no ixed osts. q q Total revenue R = 6.5q. dq 6q.75q 6q.75q = 6q.75q Rq. verage revenue R: R(q) = q = 6.75q. Total ost C = Proit = q 3q q 3.dq 3q. We write C: C(q) = 3q. q MC q. dq 3.5qdq3q.75q ; so we write R: R(q) MR 6.75* 4 3. Consumer surplus, CS() = q MRq dq.75q 6.5q 6 dq.75q. dq.375q 5. R. We illustrate all o this inormation in a diagram with the level o output on the horizontal axis and measures o ost and revenue on the vertial axis. verage and marginal revenues are downward sloping lines, with equations R(q) = 6.75q, and MR(q) = 6.5q. oth lines pass through the point (, 6) on the vertial axis, with the

8 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 marginal revenue urve twie as steep as the average revenue; marginal ost is shown y horizontal line MC(q) = 3, whih intersets the marginal revenue urve when output, q * =. This is the proit maximizing output, and we an see the onsumer surplus as the triangle ormed y the vertial axis, and the marginal revenue and marginal ost urves, whih meet at q * =. This triangle has area CS() =5. For the irm, the total ost o prodution is equal to its revenues; so that there is no produer surplus. However, it ontinues to make a proit eause it is ale to sell output at prie p= 4.5. We show the total proit, = 3, as the triangle ormed y the marginal ost and marginal revenue urves, and the vertial axis. iii. MC(q) = +.3q; MR(q) = 8.9q. I MR = MC, then +.3q* = 8.9q*, so.q* = 6; and q* = 5. We assume no ixed osts. q Total revenue R =.9q.dq8q.45q 8 8q.45q ; so we write R: R(q) = 6q.45q Rq. verage revenue R: R(q) = q = 8.45q. Total ost C =.3q.dq q.5q.5q. 5 q q q.5q q. We write C: C(q) = q +. dq 6.qdq6q.6q Proit = q MC q 5 MR 3.6* 55. Consumer surplus, CS(5) = 5 5 q MRq dq.45q 8.9q 5 8 dq.45q. dq.5q R. We illustrate all o this inormation in a diagram with the level o output on the horizontal axis and measures o ost and revenue on the vertial axis. verage and marginal revenues are downward sloping lines, with equations R(q) = 8.45q, and MR(q) = 8.9q. oth lines pass through the point (, 8) on the vertial axis, with the marginal revenue urve twie as steep as the average revenue; marginal ost is shown y the upward sloping line, with equation MC(q) = +.3q. This passes through the point (, ) on the vertial axis, and has gradient.3. It intersets the marginal revenue urve when output, q * = 5. This is the proit maximizing output, and we an see the onsumer surplus as the triangle ormed y the vertial axis and the marginal revenue and marginal ost urves, whih meet at q * = 5, and whih has area CS() = The irm makes a proit eause it is ale to sell output at prie p= We show the total proit, = 5, as the triangle ormed y the marginal ost and marginal revenue urves, and the vertial axis. X5.5 For a monopoly aing the inverse demand untion, p = q. a) Otain: i. the total revenue and marginal revenue untions; Total revenue R: R(q ) = p(q ).q = ( q ).q dr Marginal revenue MR: MR(q ) = q dq ii. the demand untion and the prie elastiity o demand (as a untion o prie). Demand untion: q : q(p) = p; elastiity o demand, p dp. q. p p dq p p p 5

9 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 ) Sketh the inverse demand urve and the marginal revenue urve. On a diagram with output measured on the horizontal axis and measures o revenue on the vertial axis, inverse demand will e shown y a downward sloping line, meeting the vertial axis at (, ), and with slope -. Marginal revenue will also e downward sloping line, passing through (, ), ut with slope, so that it is twie as steep as inverse demand. Note that inverse demand meets the horizontal axis at (, ) while marginal revenue meets the axis at (5, ). ) Indiate on your diagram the range o outputs or whih demand is elasti. Conirm that this is also the range o outputs or whih MR >. Demand is elasti when p >, or when p > 5. We note rom the diagram that when this ondition is met, q = p >5, so that MR(q ) >. X5.6 Suppose that a irm aes inelasti demand at output q. y onsidering the eet on its revenue and osts o reduing its output, show that this irm will inrease proits y reduing output. I a irm aes inelasti demand, then the responsiveness o demand to prie inreases is low; so or a monopolist reduing output, prie inreases more rapidly than output alls. Reduing output, revenues inrease, and osts neessarily all, so that proits inrease. X5.7 Using Expression 5.9, and the irst-order ondition or proit maximization, show that the prie-ost margin p MC q * [5.] MC q * Conirm that in Figure 5.4 the prie ost margin is also the ratio o proits to total osts. dq p dp q Deining elastiity =.. dp q dq p dp q dp otain MR dr q p p. p. Dierentiating the (total) revenue untion, we dq dq p dq. With proit maximization, MR(q*) = MC(q*), so that p MC q * p p. MC q * p X5.8 Using Expression 5., onirm that at the proit maximizing output, q *, the monopoly s demand untion must e elasti, or that the prie elastiity o demand, p <. Show that as p, the prie ost margin inreases without limit; and that as p, the prieost margin approahes zero. We know that or proit maximization, the proit margin must take a positive value, so that ; and so + p < ; and p < -, meaning that demand is elasti. s p -, + p p, and the prie ost margin, p MC q *. We explain this result y noting that as MC q * -, MR and so at any prie p >, the margin inreases without limit. X5.9 Given the demand untion q = p : a) Conirm that the prie elastiity o demand, p =. Prie elastiity o demand: p.. p dq dp p. q p ) Otain the inverse demand untion: and show that when =, total revenue TR(q ) =, so that marginal revenue MR(q ) =. Conirm that the monopoly then maximizes proits y setting output to zero. p

10 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 Inverse demand untion: sine p total revenue R: R = p.q = q q q, inverse demand,. So when =, R =. q p q.q q. Then we write =. Sine revenue is onstant, MR(q ) = dr dq. Sine the irm generates no additional revenue rom sales, it minimizes osts (and maximizes proits) y setting q =. ) ssume that > and that the irm has total ost untion C = q. Calulate the proit maximizing output and prie, and illustrate these in a diagram showing oth the average and marginal revenue urves and the average and marginal ost urves. dr When >, marginal revenue, MR(q ) = dq. q. With total ost, C: C(q ) = q, marginal ost, MC(q ) =. So or the proit maximizing ondition, MC(q ) = MR(q ) to e satisied, it must e that.q, and that q. Sine prie p q, we otain p q. ; and q. In a diagram, with the level o output on the horizontal axis, and measures o value on the vertial axis, the average and marginal revenues are retangular hyperolae, and so are downward sloping, onvex, and ounded y the axes. The marginal revenue urve lies loser to the origin than the average revenue urve (indeed at any level o output, q, MR(q ) = q the axis. ). The average ost and marginal ost urves are horizontal lines, a distane aove X5. Given the demand untion q = a p: a) Conirm that the prie elastiity o demand, p = p/(a p). dq p. dp q ap p p We write the prie elastiity o demand,.. ) Otain the inverse demand untion, the average revenue untion, and the marginal revenue untion. Sketh a diagram showing all o these. Inverse demand, p: p(q ) = aq R : R(q ) = p(q ).q, we write. This will also e the average revenue. With (total) revenue, aq we otain marginal revenue, MR : MR(q ) = R q q, and on dierentiating with respet to output q, aq In a diagram, with output on the horizontal axis and value measures on the vertial axis, inverse demand (average revenue) and marginal revenue are downward sloping lines, oth starting rom a, on the value axis, and the marginal revenue is twie as steep as the average revenue. ) Conirm that i the marginal revenue, MR(q ) >, then the prie elastiity o demand, p <. aq For MR(q ) >, a, so that q. ut then p(q ) > a p a a a p a a ; and ap ap a p < -.., and so d) Using the result rom part (), onirm that i the irm maximizes proits, prie p > a/.

11 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 For the irm to maximize proits, the ondition MC(q *) = MR(q *) > must e satisied, and a this an only happen i p. X5. epting the argument that Standard Oil was ale to extrat etter terms rom its suppliers than ould its potential ompetitors, explain how this might have aeted its prodution untion, giving the appearane o inreasing returns to sale in prodution. How might Standard Oil also have inreased pries to its ustomers aove the level that ompetitors might e ale to harge? [Hint: think aout the impat o lower input pries on the osts o prodution.] Negotiating etter terms with suppliers than its ompetitors, we would have expeted Standard Oil to have lower per unit (average) osts o prodution, and lower marginal osts. I these terms resulted simply rom the large volume o orders that Standard Oil was plaing, then this would e evidene o inreasing returns. However, in eet Standard Oil required its suppliers to enter into ontrats in whih suppliers had to grant those terms or else lose the ontrats; and so the terms resulted rom Standard Oil s eonomi power, rather than the sale o its ativities. X5. Suppose that a seond irm plans to enter the market. It is ale to produe a good o exatly the same quality, and aes exatly the same prodution (and ost) untions. The monopolist has already announed that i any other irm enters the market, it will inrease its output so that it just reaks even. Why would it e diiult or entry to our under suh irumstanes? Do you think that suh a poliy should e onsidered as restraint o trade? Faing the threat o entry, the monopolist proposes to expand its output, so that the market learing prie given its own and its ompetitor s output will e equal to the monopolist s average ost. We have already noted that the monopolist aes inreasing returns to sale in prodution, and thereore, assuming that is the larger irm, were the monopolist to expand output, the entrant will make losses. No entrant, who onsiders the monopolist s threat to e redile will hoose to enter the market. It may seem that the monopolist is preventing entry in this ase, ut we might also argue that the monopoly identiied a proit opportunity eore anyone else, so that the monopoly s proits relet its hoies. X5.3 Suppose that a irm does enter the market, produing an output q. Sketh a diagram showing the output o the monopolist, whih now sets output so as just to reak even. In a diagram with the monopolist s output measured on the horizontal axis, and measures o revenue and ost on the vertial axis, we show the monopolist s average revenue and marginal ost urves as eing downward sloping, with average revenue aove marginal revenue, and with oth interseting the vertial axis at the same point. We also show the average and marginal ost urves as eing downward sloping, with the average ost urve aove the marginal ost urve, and oth interseting the vertial axis at the same point. The ost urves should e latter than the revenue urves, with the average ost urve lying aove the average revenue urve at output q *, where the marginal revenue and marginal ost urves interset. We an now e ertain that the irm makes proits at output q *. llowing or entry, with the entrant s output q, the monopolist inreases its output to q, hosen so that the inverse market demand, p(q + q ) = C(q ). X5.4 We show the irm as eing ale to sell an output Q M at prie p M. pplying the argument used in X5., show that this is the welare-maximizing output. Conirm that when produing output, Q M, the monopoly makes a loss. How might government indue the monopolist to produe output, Q M?

12 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 We see that the marginal surplus rom transations at output Q M is zero; sine R(Q M ) = MC(Q M ). This is the irst-order ondition or a welare maximum. However, we also see that sine C(Q M ) > MC(Q M ), the irm makes a loss. The government ould enourage prodution at this level y providing the irm with some orm o susidy. X5.5 Suppose that the government does deide to set up a system o regulation o a market suh as energy distriution, sometimes argued to e a natural monopoly. Explain why it might e diiult or the regulator to set the prie p M, whih maximizes welare. [Hint: Think aout how easy it would e in reality to deine that prie, and also aout the impat that this orm o regulation would have upon the ehaviour o the monopoly.] To set the welare maximizing prie, p M, the regulator would need to know oth the revenue and ost untions. We might suppose that it will e possile to estimate the demand untion, ut the irm might well have inormation aout osts that it does not want to share with the regulator. In partiular, rememer that we assume that the irm always uses the most eiient omination o ator inputs. In this situation, the irm might not report ost savings that it has made through improved eiieny; or, knowing that it would not eneit rom doing so, the irm may not attempt to improve the eiieny o prodution. X5.6 In our example o the ruit market in Chapter, how likely it is that any irm would e ale to sustain a ompetitive advantage over periods o: (a) a day; () a month; or () a year? How do you think this aets the ehaviour o the irms in the market? We an e quite ertain that a day is a short enough period o time that no ompetitor will e ale to math this this is the very short run in our analysis, when the irms simply sell the stok that they have to hand. Similarly, a year seems ar too long to sustain a ompetitive advantage: other irms would have time to oserve and opy the innovation. It may well e that a period o some weeks is aout as long as a ompetitive advantage ould exist eore eing notied y other usinesses. X5.7 Why might we argue that it is essential to tolerate some degree o market power i there is to e innovation and invention in the eonomy? This uilds on the disussion o monopoly that we set out here. We have seen that market power is a transitory phenomenon in peret ompetition, have argued that there is natural monopoly where prodution is haraterized y inreasing returns to sale. There are also some servies to whih aess might e onsidered essential (suh as lean water and waste disposal); or suh usinesses, a statutory monopoly is one way ensuring provision. We an also think o market power as a generalization o monopoly power, and that it will arue to innovators. We have argued that it is diiult or innovators to make proits in highly ompetitive industries eause they lak opportunities to generate returns. This suggests that some toleration o market power may have long-run eneits in the sense o granting innovators a greater opportunity to exploit the advanes that they have made. X5.8 What justiiation, i any, would you give or eah o the ollowing measures? a) Patents these prevent any usiness other than the one holding the patent rom produing a speiied output or using a speiied tehnique o prodution. patent restrits the aility o ompetitors to exploit tehniques developed y a irm. It might redue ompetition in supply very sustantially, and so e a soure o sustantial market power. It is argued that this provides inventors with the protetion neessary or them to exploit the intelletual property inherent in their inventions, and so to earn adequate returns to their eorts. ) Copyright this prohiits the opying o a partiular expression o an idea in text or musi.

13 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 This ook is proteted y opyright, the purpose o whih is to prevent the opying o material without permission o the author (or the pulisher as my agent). gain, this is intended to give me and my pulisher the opportunity to exploit the novel expression o ideas y having a monopoly on the sale o the ook. Note that it is a very restrited right: there are many ompeting textooks, all o whih have idiosynrati harateristis, ensuring produt dierentiation. Copyright is also how omputer programmers tend to protet the expression o ideas. ) Trademarks and registered designs these restrit the reedom o other produers to opy the appearane o goods. Trademarks are perhaps the most general expression o an idea. The immediay with whih some trademarks an e reognized (the design o the Coa-Cola logo, or example) means that produers have an interest in ensuring that they annot simply e repliated. The nature o design means that this is a diiult right to assert in many ases, and the extent o the protetion oered is thereore very limited. X5.9 What might e the eets on the musi industry o the aolition o opyright? Consider in partiular the impat on the distriution o reordings and the deision to reate and perorm new material. We have started to oserve ases where artists are starting to use novel distriution platorms to disseminate musi. olishing opyright would eetively make it impossile or reordings to e made, or or musi to e sold in manusript. It would lead to musi eing marketed along with other goods, possily onneted with onert tours, estivals and other major events. We might expet there to e urther sustantial hanges in ontrol o distriution we have seen a shit rom prodution ompanies ontrolling revenues to weased distriution.

14 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 Chapter 6 X6. For prie disrimination to take plae, there must e no possiility o resale among onsumers. Explain why this ondition is neessary. Suppose that resale is possile. Then a onsumer, ale to purhase the good at a low prie, an sell it on to a onsumer willing to pay a higher prie. While we still end up with the eiient outome in whih the people who value the good most onsume it, we do reah it with a sole (inal) supplier. X6. Explain why a irm supplying personal servies, suh as a hairdressing salon or a eauty therapist, might ind it relatively straightorward to engage in prie disrimination ompared with a irm selling an easily divisile ut durale physial produt, suh as srews and nails. This turns on the question o resale. Personal servies annot e easily transerred rom the purhaser to someone else they are reated at the point o onsumption. So it is in priniple possile or a salon to harge pries that dier aross onsumers. supplier o srews and nails oers a good that an e stored and whih is also ungile srews and nails an e sold in ulk or in very small quantities. purhaser o a ulk load an thereore resell them in muh smaller quantities. X6.3 Suppose that the willingness to pay or a produt WTP(q) = 3q, while the marginal ost o prodution MC(q) =. Draw a diagram showing the average and marginal revenue urves when there is no prie disrimination, and the marginal ost urve. From the diagram alulate: () the irm s proit maximizing output in the asene o prie disrimination, and the prie that the irm then harges; () the irm s proit, and the onsumer surplus without prie disrimination; and (3) the welare loss when there is prie disrimination. Explain how the outome hanges when prie disrimination is permitted. On a diagram with irm output measured on the horizontal axis and revenue and ost measures on the vertial axis, the marginal ost urve (and the average ost urve) are oth the horizontal line, units aove the output axis. With WTP(q) representing oth the inverse demand urve and the average revenue urve (given uniorm priing), then the average revenue urve is a downward-sloping line, whih meets the vertial axis at (, ), and whih has slope -3. The marginal revenue urve is also a downward sloping straight line passing through (, ), and whih is twie as steep as the average revenue urve, so that it has gradient -6. The irm maximizes proit at output q *: MC(q *) = MR(q *); and this means that 6q * = ; so that q * = 3. The irm then harges prie WTP(3) = 9 =. The irm s proit is alulated as the area o the right-angled triangle ormed y the vertial axis, the marginal ost urve and the marginal revenue urve. This has height 8 and width 3 and so has area = ½*8*3 =,7. The onsumer surplus is the triangle ormed y the line p =, the vertial axis and the average revenue urve. This has height 9 and width 3 and so has area = ½*9*3 =,35. The welare loss is the area ormed y the triangle ormed y the line q * = 3, the average revenue urve and the marginal ost urve. s a right-angled triangle with ase 3, and height 9, this has area W =,35. ssume that we allow the irm to engage in peret prie disrimination. We redraw the diagram, simply showing the WTP urve. The monopolist ontinues sales until at output, q D, WTP(q D ) = MC(q D ). We see that then q D = 8, and the monopolist s proits are equal to the sum o the three areas stated aove: D = + CS + W = 5,4.

15 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 X6.4 Consider the situation o the irm in Exerise X6.3. The government has alulated that allowing peret prie disrimination and then olleting the tax rom the irm will ost W = 4. Should the government permit prie disrimination in these irumstanes? Yes. The potential welare gain rom trading is,35. The ost o managing prie disrimination is 4; so that there is a net gain o 95. Peret prie disrimination would e welare inreasing. X6.5 Why might it e partiularly diiult to engage in prie disrimination in sales o musi downloads? ew musiians have experimented with allowing people to download musi in return or a donation, rather than y setting a ixed prie. Explain why these experiments do not involve the pratie o prie disrimination. We have argued that resale should not e possile i there is to e prie disrimination. In priniple, it is possile to generate an ininite numer o opies o digital iles at lose to zero ost. sking or donations does not onstitute prie disrimination sine there is no prie set; while it is reasonale to allow distriution at zero prie, there is no way o onirming the WTP o donors. X6.6 Explain why it is rational or idder to respond. Suppose ids and wins the aution. So long as the winning id is less than WTP, otains surplus rom taking part in the aution. X6.7 Suppose that WTP = and WTP =. Suppose that idder responds to prie p n = How should idder respond to prie p n+ =? How does the aution end? The onditions or to id and win are satisied here; should know s valuation, then will know that any oer p n + > will win; and any oer p n + <, will generate surplus. X6.8 In a situation where there are idders, suppose that the highest valuation v () = 5 and the seond highest valuation v (99) = 48. How would you expet this aution to end? Suggest a general rule or ending the aution i it is run as a lok aution, in whih some mehanism raises the prie ontinuously, with idders hoosing the time when they withdraw rom the aution. We expet idder 99 to ontinue idding until it is impossile to enter a id o no more than 48, while idder will ontinue until it is impossile to enter a id o greater than 5. llowing ids o only whole units, we expet the aution to end with idder oering either 48 or 49. In a lok aution, we expet the idder to otain the good at a prie o 48 (or again, allowing only unit ids, perhaps 49). X6.9 Consider a slightly dierent idding proess: () Eah idder writes down a id, plaes it in a sealed envelope, and delivers it to the autioneer. () When the aution loses to urther ids, the autioneer opens the envelopes. (3) The autioneer gives the good to the highest idder. (4) The highest idder pays the autioneer the seond-highest id. Suppose that one idder still has to deide what id to make. Why might the idder regret making a id greater than WTP? [Hint: Think what happens i the idder wins.] Why might the idder regret making a id less than WTP? [Hint: Think what happens i another idder with a lower WTP wins.] What onlusions do you draw aout this orm o aution ompared with the traditional one with veral ids? id more than WTP, and it is possile to win the aution, ut, i there are two ids greater than WTP, still to pay a prie so that there the winner is worse o than y losing the aution.

16 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 Stop idding eore ids reah WTP, and is possile that the seond-highest id will e less than WTP, so that the loser is worse o than y winning the aution. We have said that in a traditional aution idders should never id more than their WTP. We see the same rule here, and so we expet the same outomes. The two orms o aution are eetively equally good or the seller. X6. Suppose that a ustomer uys only one unit o the good when the seond unit is oered or ree. What might we reasonaly assume aout the value o the seond unit to this ustomer? The seond unit has no value; WTP() <. X6. What justiiations might we give or a retailer hoosing to use this orm o promotional priing? Think in partiular aout the possile eets on its revenues, ut also onsider the impliations or its osts. With these types o arrangement, the retailer will plae a large order, suiient to otain a sustantial disount on the supply prie. This means that it does not have to sell twie as many units as it would at ull prie to maintain proits. We should also note that suh oers allow the retailer to advertise these oers, attrating more onsumers, and that, given that it sells many produts, it may well expet an inrease in sales aross the range o produts. X6. Consider the situation aing a onsumer who hooses among onsumption undles onsisting o oee and doughnuts. The prie per up o oee alls rom.5 to. on the ith up o oee. (Note that this means that the ith up o oee is eetively ree, sine the lower prie is oered on all ive ups purhased.) The prie o a doughnut remains onstant at., with no quantity disount eing oered. Sketh the aordaility (udget) onstraint or a onsumer willing to spend 4.. Disuss the diiulties that suh a onstraint might ause in trying to solve the standard optimization prolems. Show the quantity o oee onsumed on the horizontal axis and the quantity o doughnuts on the vertial axis. The onsumer an aord oees (and no doughnuts); or else doughnuts (and no oees). The aordaility onstraint passes through (, ) and (, ). Deining the slope o the onstraint as the ratio o pries, p p p d, we see that there are two segments to the onstraint. For s < 5, 5 pd, while or 5, 5 pd 3. We see that the let-hand segment o the onstraint runs rom (, ) on the vertial axis to approximately (5, 9.58); ut that there is then a disontinuity in the onstraint, so that the right hand segment runs rom approximately (5,.67) to (, ). The disontinuity means that the aordale set is no longer onvex. We annot simply rely on the irst-order ondition or maximization implied y the equal gradient ondition, ut must instead e aware o the possiility o a orner solution at the disontinuity in the onstraint; or o inding internal solutions in oth segments o the onstraint. X6.3 For the marginal onsumer, suppose that the highest attainale indierene urve touhes oth segments o the aordaility onstraint. Sketh a diagram showing this situation or a onsumer hoosing among undles o oee and doughnuts. Indiate on your diagram the eet o a small inrease in the relative prie o oee. This is possile eause the let-hand segment is steeper than the right-hand segment. It is possile to draw an indierene urve that touhes oth segments. small inrease in the prie o oee will hange the relative pries in oth segments. We might expet that this will have the eet o making one o the loal optima stritly preerred to the other, ut p

17 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 without knowing more aout inome and sustitution eets, we annot say whih this will e. X6.4 Figure 6. is inomplete. It shows that prie disrimination is possile, ut does not show that it is desirale. a) Sketh a diagram with two linear individual (inverse) demand urves, D and D, whih have dierent slopes and dierent interepts on the vertial (value) axis, and whih interset. Lael them so that the prie elastiity o demand o D is less than or D where they interset. [Hint: To make your diagram onsistent with Figure 6., make sure that you have hosen a level o marginal ost or whih onsumer would demand none o the good at prie p, so that q (p ) = ; and also so that at the minimum quantity at whih a quantity disount will e oered, Q*, WTP (Q*) < p.] ) dd the marginal revenue urves, MR and MR, to this diagram. ) ssume that the irm aes onstant returns to sale in prodution. Show its marginal ost urve; and hene identiy the proit maximizing outputs, q * and q *, and the pries, p and p, that the irm should harge eah ustomer. d) Identiy areas on the diagram that represent the proit per ustomer. How might the use o quantity disounts inrease the irm s proits? It may e useul to note at this point that demand or good is expeted to e less than demand or good. Consumer has a higher reservation prie than onsumer, and we have set up the market so that or output q *, hosen so that the inverse demand, p = p(q *) = MC =, q (p ) =. The irm oers two ontrats, one in whih the aess ee is equal to the onsumer surplus or onsumers o type : this an e shown y the triangle ormed y the marginal ost urve, the vertial axis and the inverse demand urve or onsumer. The seond ontrat requires onsumers to onsume a minimum amount, Q*, again paying a prie p. This is hosen so that onsumers o type will preer ontrat, and onsumers o type two, paying an aess ee equal to the area ormed y the marginal ost urve, their inverse demand urve and the vertial axis, preer ontrat. These two triangles represent the proit per onsumer. X6.5 On a diagram showing onsumption undles onsisting o quantities o goods and, indiate the eet o the imposition o an aess ee or good. Sketh in an indierene urve demonstrating that the onsumer would preer to pay the user ee and uy a onsumption undle onsisting o a mixture o goods, rather than simply spending the whole amount o money on good. On purhasing any quantity o good, the onsumer has to pay the aess ee. The onsumer s udget onstraint is thereore determined y the amount o money availale to inane onsumption ater payment o the usage ee. In addition, though, i the onsumer does not onsume good at all, then the amount availale to inane onsumption will inlude what would otherwise e paid as a usage ee. In a diagram with onsumption o good on the horizontal and onsumption o good on the vertial, axes, amount o money to inane onsumption, m, pries p and p, and usage pa p m,i p ee, the onstraint an e written. In the diagram, the pa m,i p m onstraint is a straight line running rom, p on the vertial axis towards, ut not quite m reahing, p on the horizontal axis. There is a disontinuity in the onstraint at =, m with the onstraint inluding the point,. p The onsumer hooses a mixture o the two goods. This means that the utility that an e derived rom some mixture is greater than the utility that an e derived rom onsumption

18 For use with Roert I. Mohrie, Intermediate Miroeonomis, Palgrave, 6 o good alone. Denote the est, aordale onsumption undle as point Z on the onstraint. Skething a smooth, downward sloping indierene urve, whih is tangent to the aordaility onstraint at point Z, we require the indierene urve to meet the m horizontal axis to the right o,. p X6.6 Explain why it is more likely that onsumers will hoose to pay the aess ee or good when the goods are omplements, rather than sustitutes. We an e ertain that the onsumer will pay the aess ee where the goods are omplements, and utility possesses the onstant elastiity o sustitution property. The relatively low value o elastiity o sustitution when goods are omplements means that indierene urves do not reah the axes; and this is suiient to ensure that the interior solution, at point Z in X6.5, will e preerred to the alternative o onsuming only good. Thinking o the example o peret sustitutes, it is o ourse possile that the onsumer will simply hoose good ; a suiient ondition eing that the marginal rate o sustitution is greater than the prie ratio, so that indierene urves are steeper than the aordaility onstraint. X6.7 Write down the preise onditions that must e satisied in order or the two onsumers to hoose the dierent supply ontrats. There are two onditions whih must e satisied or oth Omar and Paul. Omar must preer ontrat to oth ontrat and staying out o the market. Paul must preer ontrat oth to ontrat and staying out o the market. For Omar, CS O (, p ) max{cs O (, p ), }, while or Paul, CS P (, p ) max{cs P (, p ), } X6.8 Consider the situation aing a ar manuaturer. It elieves that its ustomers onsider ars to e a undle o harateristis, whih we summarize as speed and omort. ssume that the irm has to trade o these harateristis, so that eah model o ar is loated at a partiular point on a prodution possiility rontier, whih shows easile ominations o speed and omort. a) Sketh a diagram with a onave prodution possiility rontier. In a diagram with maximum speed measured on the horizontal axis and omort measured on the vertial axis, we show the prodution possiility rontier as a downward sloping urve, whih, moving rom let to right, eomes inreasingly steep. ) Suppose that the irm produes our models. Explain how doing so would allow the irm to meet the desires o onsumers with dierent preerenes. In the diagram, we an show dierent preerenes through dierenes in the gradient o indierenes urves through any harateristis undle, and eetively dierenes in the marginal rate o sustitution o omort or speed. The steeper the indierene urve, and so the larger the marginal rate o sustitution, the loser the harateristis undle at whih the irst-order ondition that the prodution possiility rontier and the indierene urve share a ommon tangent will e to the horizontal (speed) axis. Suh onsumers preer ast ars. Similarly, the latter the indierene urve, and so the smaller the marginal rate o sustitution, the loser the harateristis undle at whih the irst-order ondition that the prodution possiility rontier and the indierene urve share a ommon tangent will e to the vertial (omort) axis. Suh onsumers preer omortale ars. Note that with the indierene urves releting well-ehaved preerenes, so that they are onave, the intersetion o eah onsumer s aordale and preerred sets is again the single harateristis undle ormed y the most-preerred easile undle. We might also note here that with well-ehaved preerenes, we do not need the tangeny ondition to e satisied. Suppose that Rita has a stronger preerene or speed to Sandy, and