PROBLEM SET 1 (Solutions) (MACROECONOMICS cl. 15)

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1 PROBLEM SET (Solutions) (MACROECONOMICS cl. 5) Exercise Calculating GDP In an economic system there are two sectors A and B. The sector A: - produces value added or a value o 50; - pays wages or a value o 30; - sells intermediate goods to sector B or a value o 5. In the same year sector B: - purchases intermediate goods rom sector A or 5 and rom abroad or a value o 0: - pays wages or a value o 0; - sells inal goods or a value o 40 o which 0 goes abroad; - sells investment goods or a value o 0 o which 5 goes abroad. Compute the GDP o this economic system by describing and explaining the possible deinitions that can be employed. With the inormation we have we can compute GDP by using the ollowing deinitions:. As the sum o each sector s value added: V.A. A 50; V.A. B (40 + 0) (5 + 0) 5 GDP As the sum o incomes distributed inside the economic system: Proits A revenues intermediate goods purchases wages taxes values added - wages ; Proits B (40 + 0) (5 + 0) 0 5 Wages A 30 ; Wages B 0; Taxes 0 GDP Exercise The paradox o saving Consider the ollowing model: Y C + G + I C c + 0 cy d T 50 G 50 I 00 with c 0 0 and c. a) Compute equilibrium income consumption and savings. b) Suppose the government asks consumers to save more. The consumers abide and reduce c 0 by 5. What happens to equilibrium income consumption and saving? Explain the intuition. a) The equilibrium short term production is derived by solving: Z C + I + G Y Z. Following the same steps as in previous exercise Y (Y 50) Y Y Y 35 Y 470 C (470 50) 0 S Y T C

2 OR Y ( c0 + I + G ct ) Y c and by substitution C ( ) 0 S Y T C [ ( 50) ] b) The government request entails a reduction in autonomous expenditure equal to the variation in c autonomous consumption: 0 5. Thereore the new values o Y C and S are: Y ' [ ( 50) ] C' 5 + ( ) 0 S ' Savings remain constant since rom the relation S Y T C we know that C S. C Z Y Y S Nevertheless we also know that d. Thereore at irst sight the net eect is ambiguous. However knowing that the relation S I + ( G T ) holds and since I G and T are unchanged the two eects must cancel out (savings paradox). N.B. Since production is a linear unction o autonomous expenditure its variation could also have been calculated using partial derivatives: Y Y ( 5) 0 Y ' Y + Y Exercise 3 - The money market In country A the quantity o money (M) in the year 000 was equal to 450 billion euro. In the same year the ratio o money held in currency (c) and the ratio o reserves/deposits (θ) took on the ollowing values: c 0. and θ 0.4. a) Compute the supply o central bank money in 000. b) What is the money multiplier? c) Suppose the central bank can perectly control the value o the ratio reserves/deposits (θ). I in 00 the central bank wanted to increase the money supply to 675 billion euro by how much must θ vary i H and c remain constant at their 000 levels? a) The relation between central bank money and the overall money supply is: H M [ c + θ ( c) ] Substituting the values we have: H 450 [ ( 0.) ] H 450 H 34 b) The money multiplier is c + θ ( c) ( 0.) [ ] [ ].93

3 c) To determine the variation in the reserve/deposit ratio (θ) coherent with the objectives o the central bank we use the equation that relates central bank money and the overall money supply: [ 0. + θ ( 0.) ] 675 [ θ ] θ θ Hence the needed variation is θ θ θ Exercise 4 Fiscal Policy Consider the ollowing numerical version o IS-LM model: C Y d I i + 0.Y G 00 T 00 M d /P Y 7500i M s /P 500 a) Calculate the equilibrium level o income and interest rate. b) Suppose the government increases public spending to 300 ( G 00). Compute the new equilibrium values o income and interest rate. c) Suppose the government decreases taxes to 00 ( T -00). Compute the new equilibrium values o income and interest rate. d) Compare the results you have ound in (b) and (c). Provide an economic explanation or the variation. I the government wants to inance the change in G by increasing T same amount ( T 00) what happens to the economy? a) It is necessary to have the equilibrium in both goods market and the money market. Equilibrium condition or goods market is Y C + I + G (IS) d s M M Equilibrium condition or money market is P P Goods market: Y Y d i + 0Y + 00 Y (Y 00) i + 0Y + 00 Y Y i + 0Y Y i Y i IS Money market: 05Y 7500i 500 LM We insert the IS equation we ound above (Y i) into the LM equation and solve or i. 05( i)- 7500i i 7500i i i 008 8% Then we insert the equilibrium interest rate to the IS equation to be able to ind the equilibrium Y

4 b) Y (008) Y 00 Y ( c d ) + d (iscal policy multiplier or Y) where A c0 + I + G ct is autonomous expenditure. G Y *00.5* ( 0.) Y Y + Y i Y (iscal policy multiplier or i) ( c d) + d ( c d) + d i ( 05 0) i 00 i i 0 + i %. OR You can use the same methodology we used in point (a) and solve the equations again by inserting G300 instead o G00 An increase in G is an expansionary iscal policy and it causes IS curve to shit right. As a result equilibrium values or both Y and i increase. c) T -00 -c T -(05)(-00 ) Y *50.5* ( 0.) Y Y + Y i ( 05 0) i 0005 i i 0 + i %. OR You can use the same methodology we used in point (a) and solve the equations again by inserting T00 instead o G00 A decrease in T is again an expansionary iscal policy and it cause IS curve to shit right. As a result equilibrium values or both Y and i increase. d) Both in point (b) and in point (c) we have an expansionary iscal policy. In point (b) it is through increasing public spending and in point (c) it is through a reduction in taxes. It can be observed that although the amount o increase in G and decrease in T are same in absolute terms their impact on equilibrium Y and i are dierent. An increase in public spending has higher impact on equilibrium values than a reduction in taxes. This is due the act that G enters the equation directly as an autonomous expenditure while changes in taxes aect the equilibrium levels through the inluence on disposable income.

5 I the government wants to inance the change in G by increasing T same amount ( T 00) increasing T by the same amount would not help to return to the initial equilibrium because o the reason discussed above. Changes in T aect the equilibrium income through its impact on disposable income while changes in G have a direct impact. So i the government wants to inance the change in G it should increase T more than the increase in G. In our example c 05 so the increase in T should be equal to: Gc T T T 00