Question

A closed economy can be described by the long-run classical model:

Y = 2K^αL^1–α

C = 18500 + 0.75(Y – T) – 800r

I(r) = 11000 – 1200r

Note: r represents the real interest rate and is measured in percentage points (for example, if we find r = 10, then r is interpreted as being equal to 10%). Keep your answer to 4 decimal places if needed.

Assume that there are two factors of production, capital (K) and labour (L), and that they are both fully employed. For this economy the supply of capital and labour are 27000 and 64000 respectively; and one-third of output goes to capital owner. Initially, the government collects 6% of the economy’s (long-run) output as (income) taxes, and the size of the budget deficit is 540.

1. Compute the long-run equilibrium levels of consumption, investment and private savings. Also, find the long-run equilibrium real wage for labour.  
2. Suppose the newly elected government wants to set the equilibrium level of national savings to 9104 via a change in (income) taxes. Find the level of taxes that will achieve the goal. What happens to the level of private savings (i.e., does it change? By how much).  

Now, return to the initial long-run equilibrium as shown in part (a). Suppose there is a downward adjustment in the stock market. As a result, autonomous consumption falls by 10%.

3. Why does autonomous consumption fall when there is a downward adjustment in the stock market? Explain in words
4. Find the new long-run equilibrium levels of consumption and private savings.  
5. Use the diagram for the loanable funds market to show your findings in parts (a) and (d). Be sure to clearly identify the equilibrium to each part of the question in your diagrams. No written explanation is needed.  

Answer 1

owne a a) As Yз of output goes to capital 3 Уз :. Te 2к"L -2 (2чо0о (е40oоуs Уз E2х х Б160 оо6 >хg600 о 3 54O - a -т Now, Bwdat defiui 5960 + 540 = 6300 :. Cл G T: са+ I — во0 т ( n6000- 5 18500t o' 75 -Со t 11000- 1200Y 1о3480 2000 r - 10 3480 -a6 000 2000 7480 3'74 о001 800 ( 3.14) - .. С в 1850о+ 67680 8 3188 6512 200 3 4) = П000- 5 3 6O 831 88- Y- с - т а 9600 0 - Sp F052 -ва (+- 1 Уз K :MPL 2

Before the national soauings was: SG Sp 512 In order to increase S to 10A AS = 259 2 Tham tne wriu achiewe Anin 'n Ti tax thak - с -т, t Ti- a 89700 - C Y - C a104 2000Y 7300 Yz18600tg'T5(96OBO-T7 IO78O0 3 O 5a6 tI1000 - 1200 Yr t 6300 a6ooo .. Y : I'58 Ti)-800(sa) 8 500 t o*75 (960oo- C 2 36 + F q20 00 - O'75 T 892 36 - o'75 T 80 596 8 640 I1 520 96000 -80 596-11 52о Sp 3884 wnit) 316 8 :. ASp 3168 adinstment Fa in interasi decreases vau decreases down ward C The ntercesi rafe . vead vau wealth of the osawings and they decreases thein autohomo ws consumption. consumex. dhun

consumption: New - 8 O0 r C 66 50t o'75 (Y- T) New eawi ibri umm '. I C t 2 O O O Y ...^6 600- 5 6 30 .. 2000 Yr 2:815 :. Y 32078 8 16 2 . Sp 334 2-815 S LF