University of Bath DEPARTMENT OF ECONOMICS COURSEWORK TEST 1: SUGGESSTED SOLUTIONS

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1 University of Bath DEPARTMENT OF ECONOMICS COURSEWORK TEST 1: SUGGESSTED SOLUTIONS First Year INTRODUCTORY MICROECONOMICS (ES10001) 3 RD NOVEMBER 2017, 17: (75 minutes) ANSWER ALL QUESTIONS The coursework test aer comrises four ages an is ivie into two sections: Section A (True / False) contains five questions at 6 marks er question (total 30 marks); Section B (Multile Choice) comrises seven questions at 10 marks er question (total 70 marks). The examination aer thus comrises 100 marks. Note: An incorrect answer will result in a ten er cent reuction in the mark available for the question; thus an incorrect answer to a true / false question will result in a reuction of 0.6 mark an an incorrect answer to a multile choice question will result in a reuction of 1 mark. CANDIDATES MUST NOT TURN OVER THE PAGE AND READ THE TEST PAPER UNTIL INSTRUCTED TO BY THE CHIEF INVIGILATOR PLEASE WRITE BOTH YOUR CANDIDATE NUMBER AND THE LETTER SET OUT IN THE BOTTOM RIGHT HAND CORNER OF THIS PAGE ON YOUR ANSWER SHEET ANSWER PAPERS WITHOUT EITHER WILL NOT BE MARKED THIS QUESTION PAPER MUST BE HANDED IN WITH THE SCRIPT AT THE END OF THE TEST A 1

2 Section A: True / False (6 marks er question) 1. If there is no enowment effect, then the eman curve for a Giffen goo is always uwar sloing: A. TRUE B. FALSE Solution: Assume the consumer consumes a bunle of goos x = ( x 1,x 2,...,x n ) an assume that goo 1 is Giffen. Define!x 1 = m! 1 as the maximum quantity of goo 1 that the consumer can consume at rice! 1 given his buget income m. Any 1 >! 1 imlies x 1 <!x 1 in orer for the buget constraint to be satisfie. Intuitively, if eman increases with rice, an if the rice rises to such an extent that the consumer is evoting all of his buget income to the consumtion of that goo, then any further increases in rice must result in a ecrease in consumtion of goo 1 such that the eman curve for goo 1 becomes ownwar sloing (i.e. backwar bening). 2. In the country Janlania the whole oulation eat one meal a ay, choosing either chocolate ie or vegetable curry. Everyone has ientical income an tastes. Chocolate ie is the cheaer meal an is an inferior goo for everyone. The Janlanian Government is consiering imosing an unhealthy foo tax on chocolate to reuce chocolate consumtion. But an exert aviser argues that chocolate consumtion will efinitely increase if its rice goes u. The exert is correct: A. TRUE B. FALSE Solution: Chocolate ie is an inferior goo so an increase in its rice will lea to a fall in the eman for chocolate ie via the substitution effect but an increase in the eman for chocolate ie via the income effect. Thus the overall effect of the eman for chocolate ie is ambiguous. If the income effect ominates the substitution effect, then the overall eman for chocolate ie will increase. But this is not certain an so the exert is incorrect. 3. If in a two goo worl, goos x an y are comlements for one another at all ossible ( ), then the own rice elasticity of eman, Ε = q rices x, y each goo is greater than one at all ossible rices: A. TRUE B. FALSE Solution: Consier goo x an efine the own rice elasticity of goo x as: Ε x = x x x x Further, efine the buget constraint as: ( )( q) > 0, for 2

3 x x + y y = m Now, hol y an m constant an consier a change in x : ( ) m = x + y x y = 0 x x 1 x + x x x + y y x = 0 Thus: y = 1 x + x x y x x y = x 1+ x x x y x x y x = x y ( Ε x 1) If the two goos are comlements for one another then ( y x ) < 0 which (assuming x > 0 an y > 0 ) imlies that Ε x < 1. Intuitively, if Ε x < 1 then a one er cent increase in the rice of goo x will lea to a less than one er cent ecrease in the eman for goo x such that exeniture on goo x increases. If the rice of goo y an money income remain constant, then sening on goo y must fall, which imlies that the eman for goo y falls. 4. Ben sens all of his income on green eggs an ham. Green eggs are an inferior goo for him. If his income increase by 25 er cent an rices i not change, then his exeniture on ham must have increase by more than 25 er cent of his original income: A. TRUE B. FALSE Solution: Write Ben s original buget constraint as: x x + y y = m where x enotes green eggs an y enotes ham. His new buget constraint may be written as: x x + y y = m 3

4 where x < x by inferiority. Thus: ( ) = ( m m) x ( x x) y y y y Δy = Δm x Δx y Δy = 0.25m x Δx y Δy > 0.25m since Δx = x x < 0. Intuitively, since green eggs are an inferior goo then it must be the case that Ben reuces his consumtion, an thus exeniture, on green eggs as a result of the 25 er cent increase in money income. To maintain his buget constraint, Ben must have increase his exeniture on ham by more than 25 er cent eole live in the village of Barton-uner-Wol. In 2017 the village will celebrate its 1000 th anniversary. As art of its celebrations the Parish Council is consiering whether to stage a fireworks islay, which woul cost 19,000. The Council has surveye of the resients, asking them the maximum they woul be willing to ay to atten the islay. Their resonses were all ifferent, varying uniformly from lus 20 to minus 5 - some resients (e.g. et owners) resone with a negative rice since they woul ay for the islay not to take lace. From their maximum willingness to ay resonses the Council has constructe the following eman function: q ( ) = where q ( ) enotes the number of resients who woul be willing to ay at least rice! to atten the islay. The Council ecies that it will run the islay an recou the cost by increasing local taxation if an only if this increases the net well-being of its citizens. The Council is non-corrut an is seeking only to maximise the well-being of the resients, an the resients answere the survey honestly. The Council ecies to run the fireworks islay. A. TRUE B. FALSE Solution: See Figure 1: 4

5 20 A B C D q -5 E The normal eman function imlies: q ( ) = ( q) = 20 q 100 Figure 1: Villagers Deman for Firework Dislay The resients woul therefore obtain a total consumer surlus from the islay of: Area ABC Area CDE CS = ( ) ( 5 500) Thus, the Council shoul not go ahea with the islay. Section B: Multile Choice (10 marks er question) = < The weekly eman an suly functions for wine urchase in UK suermarkets an other retail outlets are: q q s ( ) = 50 5 ( ) =

6 where enotes rice er bottle an q enotes millions of bottles er week. The government imoses a sales tax of 3 a bottle. Ignoring costs (e.g. health) arising from alcohol consumtion, the tax reuces society s net welfare by: A. 75 million a week B. 50 million a week C. 40 million a week D. 15 million a week E. None of the above Solution: The eman an suly functions imly: q ( ) = 50 5 ( q) = 10 q 5 An: q s s ( ) = ( q) = 1+ q 10 Original equilibrium: ( q ) = 10 q 3 10 q = 9 q = 30 5 q = = ( s q ) An: ( 30) = = 4 30 = 4 = = ( s 30) After the tax: 6

7 ( q t ) = 10 q t 3 10 q = 6 t q t = 20 ( ) + q t 5 = = t s ( q t ) An: ( 20) = t = 6 See Figure 2: 10 5 = 6 = 1+ 3 ( ) = s 20 t ( ) t s A C B t = 3 s q Figure 2 Net welfare is efine as CS + PS + T, where T = tq. It is aarent that this is reuce by the triangle ABC where: Area ABC = =

8 7. There are 3 consumers (1, 2, 3) of goo x. Each consumer has a unique eman function: q 1 ( ) = 10 q 2 q 3 ( ) = ( ) = 20 for < for for > for < 20 0 for 20 The suly function for the goo is: q s ( ) = 5+10 Which grah illustrates the inverse total suly an inverse eman functions for goo x? A. Figure A B. Figure B C. Figure C D. Figure D E. None of the above s s 0 q 0 q Figure A Figure B 8

9 s s 0 q 0 q Figure C Figure D Solution: At any > 40 we have: q 3 ( ) q i i=1 ( ) = q 1 ( ) = 10 At any we have: q 3 ( ) q i i=1 ( ) = q 1 At any < 20 we have: ( ) + q 2 ( ) = 50 q q ( ) = q i Note that: q s i=1 ( ) = 5+10 ( ) = q 1 s ( q) = q ( ) + q 2 ( ) + q 3 ( ) = It is aarent that s ( 10) = = 0.5 < 40 an s ( 30) = = 2.5 < 20 such that the equilibrium must lay on the lowest segment of the aggregate eman curve vis. s ( 117.5) = = see Figure 3: 9

10 q ( ) = q 1 ( ) = s q = q 1 + q 1 = q = q 1 + q 2 + q 3 = q Figure 3 8. Ben sens his entire buget an consumes 19 units of x an 18 units of y. The rice of x is three times the rice of y. His income oubles an the rice of y triles, but the rice of x stays the same. If he continues to buy 18 units of y, what is the largest number of units of x that he can affor? A. 42 B. 32 C. 22 D. 12 E. None of the above Solution: Consier first Ben s original buget constraint: 19 x +18 y = m 57 y +18 y = m m = 75 y since x = 3 y. Now, let θ enote the largest number of units of x that Ben can affor if he continues to buy 18 units of goo y when his income oubles an the rice of goo y triles: 10

11 θ x + 54 y = 2m 3θ y + 54 y = 150 y 3θ + 54 = 150 3θ = 96 θ = Ben an Grace have the same, stanar convex references over income an leisure an are free to chose how many hours to work each ay. Ben is ai 10 an hour an chooses to work 9 hours a ay. Grace is ai 9 an hour for the first 8 hours she works an 18 an hour for any time she works beyon 8 hours a ay. Which of the following statements is comletely true? A. Since she has the same tastes as Ben an can earn the same income by working 9 hours a ay, Grace chooses to work 9 hours a ay B. Ben woul be better off facing the same ay scheule as Grace C. Grace woul refer Ben s ay scheule to her own D. Grace will work less than 9 hours a ay E. None of the above Solution: Ben s (linear) ay scheule imlies a maximum income of 10*24 = 240. Grace s (kinke) ay scheule imlies a maximum income of 9*8 + 18(24-8) = 360. It is aarent that the two scheules intersect at T-9 hours since 10*9 = 90 = 9*8 + 18*1. Since Ben an Grace have ientical references an thus ientical inifference curves, then Ben woul be better off facing the same ay scheule as Grace See Figure 4: 11

12 360 m E E 90 0 I 1 I h h. 9..h. T-9 T-8 T=24 L Figure The eman for wheat in Tucklan is q ( ) = 24. There are no imorts or exorts of wheat. The suly of wheat in Tucklan eens on the weather in the growing season. In a goo year the suly is q s ( ) = an the Government imoses a sales tax of 1.50 er unit of wheat. In a ba year the suly is q s ( ) = an the Government rovies a subsiy to suliers of 1.50 er unit of wheat. The total tax collecte by the Government in a goo year excees the total subsiy ai by the Government in a ba year by: A. 3 B. 5 C. 7 D. 9 E. None of the above Solution: First, note the inverse eman curve: q ( ) = 24 (q) = 24 q Now, consier the inverse suly curve in a goo year. Without the tax, we have: 12

13 q s ( ) = s (q) = q With the tax, we have: q s ( ) = s (q) = q s t (q) = ( 3+ t) + 0.5q t s (q) = q Thus, in equilibrium: (q t ) = 24 q t = q t = t s (q t ) 48 2q t = 3+ q t 3q t = 51 q t = 17.5 Thus tax revenue collecte is T = tq t = = Now, in a ba year, we have: q s ( ) = s (q) = q With the subsiy, we have: s s (q) = ( 3 s) + 0.5q s s (q) = q Thus, in equilibrium: 13

14 (q s ) = 24 q s = q s = s s (q s ) 48 2q t = 3+ q t 3q s = 45 q s = 15 Thus subsiy rovie is S = sq s = = There are only two goos, goo 1 an goo 2. When rices are 2 an 2, Grace sens her entire income of 12 on quantities x 1 = 3 an x 2 = 3. Her own rice arc elasticity of eman for goo 1 is 1 3 over the range of rices 1 = 2 to 3. The rice of goo 1 increases from 1 = 2 to 1 = 3. In the new equilibrium Grace urchases what quantity of goo 2? A 6 7 B C D E. None of the above Solution: Initial situation: 1 x x 2 = M ( 2 3) ( ) = 12 Now, for goo 1: 1 = 1 = 2 = 14

15 Ε 11 = Δx 1 Δ 1 1 x 1 Ε 11 = x = ( x 1 x 1 ) ( ( ) ) 2 ( x 1 + ) 2 = ( ) ( ( ) 2 + 3) 2 ( 3+ ) 2 = 1 3 Ε 11 = 3 x x 1 ( ) = 3+ x x 1 = 3+ x x 1 = = 21 8 x 1 x 1 ( ) 2 = 1 3 Thus, in the new equilibrium: 1 x x 2 = M ( ) + 2 x x = 96 x = ( ) = 12 x Grace insists on consuming 4 times as much of y as she consumes of x (so she always has y = 4x). She will consume these goos in no other ratio. The rice of x is 3 times the rice of y. Grace has an enowment of 20 x s an 45 y s which she can trae at the going rices. She has no other source of income. What is Grace s gross eman for x? (7 oints) A. 105 B. 65 C. 15 D. 12 E. None of the above Solution: First, ascertain Grace s buget line. Her initial enowment is ( x, y) = ( 20,45) an x = 3 y. Thus, Grace coul sell all of her 20 units of goo x an acquire an aitional 60 units of goo y, or alternatively, sell all of her 45 units of goo y an acquire an aitional 15 units of goo x. Thus, her buget line is efine by the equation: 15

16 y x = 105 3x An we know that her references imly that she will only consume where: y = 4x Thus, her utility maximising bunle is where: y = y y = 105 y = y = 60 Such that: x = y 4 = 60 4 = 15 See Figure 5: 16

17 105 y y = 105-3x y = 4x I * x Figure 5 17