Suppose the United States (closed) economy is represented by the following equations:

Y = C + I + G

C = 500 + 0.5 (Y T)

I = 2, 200 200r

G = 1, 000

T = 1, 000

(a) Given the above variables, and assuming that r = 1, calculate the equilibrium level of

output.

(b) Now, assume that government spending increases from 1,000 to 1,100 (while taxes

remain at 1,000). Calculate the new equilibrium level of output. How much does income

change as a result of this event?

(c) Now, assume that instead taxes increase from 1,000 to 1,100 (while government spending

remains at 1000). Calculate the new equilibrium level of output. How much does income

change as a result of this event?

(d) Suppose the government is required to have a balanced budget by law (T G = 0).

Now, assume that the government decides to increase government spending from 1,000 to

1,100 and at the same time to raise taxes from 1,000 to 1,100 (these two policies together

will still result in a balanced budget: T

0 G0 = 1, 100 1, 100 = 0).

i. Calculate the new equilibrium level of output. Is this combination of policies expansionary, contractionary, or neutral with respect to output? Explain briefly.

ii. Can you explain the result in the previous part? (Hint: Look at the general expression

that you used to derive equilibrium output and focus on how taxes and government

spending enter this equilibrium condition.)

iii. Graphically illustrate your result (of the "budget-neutral" policy of a simultaneous

government spending increase financed by a tax revenue increase of equal size) in a

loanable funds market diagram.

2. Consider the Solow model of economic growth. You are given the following equations:

Y = C + I

C = (1 s)Y

Y = F(K, EL) = K

1

3 (EL)

2

3

where Y = real aggregate GDP; C = real aggregate consumption; s = saving rate with 0 <

s < 1; K = aggregate capital stock; L = working population; and E = the efficiency of labor.

Capital depreciates at rate , the working population grows at rate n, and the efficiency of

labor (labor-augmenting technical progress) grows at rate g.

(a) Briefly, in one or two sentences, explain each equation.

(b) Define k

K

EL , y

Y

EL , and i

I

EL . Derive (i) the equation that gives y as a function

of k and (ii) the function that gives i as a function of k. (iii) Write down and explain the

equation that describes the dynamic behavior of k, (that is, the equation that describes

k).

(c) Illustrate these two functions in a diagram. Use the diagram to explain how and why the

economy converges to a long-run steady state equilibrium.

(d) Suppose the current saving rate, let's call it s0, leads to a steady state capital stock that

is higher than the "Golden Rule" capital stock. How should this economy adjust its

saving rate in order to eventually transition to the "Golden Rule" capital stock? Describe

verbally and in a diagram what happens to the growth rate of output per effective

worker y, and to the level of output, investment and consumption during the transition

period.

Consider the model of long-run equilibrium in a closed economy as given in Chapter 3 of the

text. Use diagrams of the labor market, the market for capital, and of output as a function

of labor inputs to show how a decrease in the supply of capital (caused, for example, by

an earthquake) will affect the equilibrium values of output, employment, the real wage, the

marginal product of labor, the capital stock, and the real rental price of capital. You may

assume that the labor supply curve is vertical.