Model of a closed economy

Question

Problem 1. Use the following model of a closed economy to answer this set of questions.

Y = C + Sp + (T - TR)

Sg = T - TR - G

NS = Sp + Sg = Y - C - G

Y = C + I + G

Y = AK^1/2L^1/2

C = 20 + .5 (Y - (T - TR))

In this economy A is equal to 2. You are also told that capital, K, is fixed in this economy and equal to 100 units and that the labor market is characterized by the following labor demand and labor supply curves where L is units of labor and W is the wage rate:

Labor Demand: L = 200 - 10W

Labor Supply: L = 10W

You are also told that government spending, G, is equal to 50 and that the government is running a balanced budget.

a. What is the value of aggregate production in this economy? In your answer show the work necessary to find your answer.

b. What is the level of consumption spending in this economy? In your answer show your work for computing this value.

c. What is the value of investment spending in this economy? Show your work.

d. What is the value of private savings, Sp, in this economy? Show your work.

Problem 2. Use the information and model you have in problem (1) to answer this question. Suppose that the labor market and aggregate production function are unchanged, but that government spending increases by 10 while net taxes, T - TR, are unchanged.

a. Is the government running a budget deficit or budget surplus? Give a numerical value for the government's budget balance.

b. What is the value of investment in this economy given the change in government spending?

c. Describe in words the effect of this change in government spending on C, Y, I and NS.

Now, suppose this economy opens to trade and it runs a trade surplus equal to 20.

d. What is the value of capital inflows, KI, into this economy?

e. Now that this economy is an open economy, identify all the potential sources of loanable funds in this economy?

f. Assuming that the loanable funds market is in equilibrium, what is the value of investment in this economy now that it is an open economy? Show your work.

Problem 3. Use the following model of a closed economy to answer this set of questions.

Y = C + Sp + (T - TR)

Sg = (T - TR) - G

NS = Sp + Sg = Y - C - G

Y = C + I + G

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

C = 20 + .5(Y - (T - TR))

Sp = -20 + .5(Y - (T - TR))

I = 110 - 5.5r

Demand for labor: L = 200 - 10W

Supply of labor: L = 10W

a. Assume initially that the government's budget is balanced and that the level of government spending is equal to 50. Also, capital, K, is fixed in this economy and equal to 100 units. What is the equilibrium interest rate and the equilibrium level of investment in this economy? Show your work and provide a verbal explanation for how you get your answer.

b. Suppose the government increases government spending to 60 but does not change its tax and transfer policy. What is the effect of this change in government spending on Y, C, I, the government's budget balance, and the interest rate? Before calculating numeric values provide a qualitative description (use the table below) of what you think will happen to these variables.

My qualitative predictions for these variables are given in the following table (predictions should be "no change", "increases", or "decreases"):

Variable	Direction of Change	Reasoning Behind Prediction
Y
C
Government's Budget Balance
I
r

Now, calculate numeric values for each of the above variables.

c. Suppose that the country now opens to trade and it runs a trade deficit equal to 20. Government spending is still equal to 60 with no changes to net taxes. What do you predict will happen to I and r? Calculate specific values for I and r.

d. Given the information you had in part (c) of this problem, what will happen to I and r if the government increases its spending to 80 while maintaining the same tax policy? Make a prediction and then calculate numeric values.

Problem 4. Use the following information to answer this question.

Investment Demand Function for Loanable Funds Market: I = 2000 - 100r

Private Savings Function: Sp = 125r - 250

Demand for Labor: L = 200 - 10W

Supply of Labor: L = 10W

Aggregate Production Function: Y = 20K^1/2L^1/2

Available capital in economy: K = 100

(T - TR) = 50

KI = M - X = 0

Sg = 0

a. What is the level of aggregate production in this economy? Show your work.

b. What is the equilibrium interest rate and equilibrium level of investment for this economy? Show your work.

c. What is the level of private saving, Sp, and consumption, C, in this economy?

Now, suppose that government spending increases to 100 with no change in tax policy or the foreign sector.

d. What happens to C, I, r, and Y with this change in government spending?

Now, suppose government spending is still equal to 100 with no change in tax policy. But, suppose this economy now runs a trade deficit equal to -200.

e. Given the above information, make a prediction about each of the following variables. Your predictions should be "no change", "increases", or "decreases". Use the following table to organize your answer.

Variable	Prediction
Y
C
Sp
I
r

f. Given the changes described in part (e) calculate actual numeric values for Y, C, Sp, I and r.

g. Fill in the following blanks assuming an upward sloping private savings function.

i. Holding everything else constant, in the loanable funds market an increase in government spending _____________ the interest rate, _________ the level of investment and _______the level of private saving.

ii.                  Holding everything else constant, in the loanable funds market an increase in net exports will _____________ the interest rate, _______ the level of investment, and __________ the level of private saving.

Problem 5. Assume that capital accumulation in the economy of country X follows the following pattern.

K_t+1=K_t -δK_t  + I_t

I_t=.2K_t

In the expression above K_t is capital in the current period, K_t+1 is capital the next period, I_t is current investment, and delta, δ, is the fraction of capital that depreciates in the current period.

Assume this economy has an initial level of capital of 100.

a. Using Excel graph the behavior of capital over the next 60 periods assuming delta is 0.10.

b. Using Excel graph the behavior of capital over the next 60 periods assuming delta is 0.21.

c. Referring to the graphs above explain how investment affects capital accumulation over time given different levels of depreciation.