Question 2 (30 points) - Chapter 3

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

Y = 5K^1/3L^2/3

C = 12500 + 0.75(Y-T) - 325r

I = 25000 - 500r

In this economy, there are two productive factors, K and L and both factor inputs are fully employed.The stock of capital and the supply of labour are equal to 8000 and 3375 respectively.Initially, the government collects 20% of the long-run level of output from households as taxes and it runs a balanced budget.

Note: r represents the real interest rate and is measured in percentage points (for example, if r = 10, then this is interpreted as r = 10%). Keep your answers to4 decimal pointsif needed.

a)Compute the long-run equilibrium levels of consumption, investment and real interest rate.Also, find the real wage for labour and real rental price of capital.(6 points).

Now, suppose households suddenly become more optimistic about the future such that autonomous consumption increases by 1650.

b)What are the new long-run equilibrium levels of consumption, investment, and real interest rate?Compute the new long-run equilibrium real wage rate for labour and real rental price of capital.(6 points)

c)Show your answer for parts (a) & (b) in three diagrams (that depict the loanable funds market, the labour market, and the rental market for capital).Be sure to identify which points on your diagrams are the equilibriums for part (a) & (b) respectively.No written explanation is required.(6 points)

d)Suppose the government finds the change in the long-run equilibrium level of investment in part (b) undesirable and wants to use government spending on goods & services to keep investment at its initial long-run equilibrium level (i.e., the one in part a).Can the government achieve this goal?If yes, find the level of government spending that could achieve this goal.What happens to the government budget balance?If no, explain why.(6 points)

e)(Ignore part d) Suppose instead the government finds the change in the long-run equilibrium level of real interest rate in part (b) undesirable and wants to use government spending on goods & services to set it to 35%.Can the government achieve this goal?If yes, find the level of government spending that could achieve this goal.What happens to the government budget?If not, explain why.(6 points)