Question 1 (10 points)

Does a fixed-weight price index like the CPI underestimates or overestimates the change in the cost of living? Explain.

Answer: A fixed-weight price index like the CPI does overestimates the change in the cost of living because it does not take into account that people can substitute less expensive    goods for ones that have become more expensive.

Question 2 (5 points)

Assume that equilibrium GDP (Y) is 5,000. Consumption (C) is given by the equation C=  500+0.6Y. Investment (I) is given by the equation I=2,000– 100r, where r is the real interest rate, in percent. In addition, assume that G=0. Solve for the equilibrium real interest rate.

Answer: Y = C + I + G + NX G=NX=0 Y = (500 + 0.6Y) + (2,000 − 100r) Y=5000 5000 = 500 + 0.6(5000) + 2,000 − 100r → 500 = 100r → r = 5

Question 3 (15 points)

Consider two competitive economies that have the same quantities of labor (L = 400) and capital (K = 400), as well as the same technology (A = 100). The economies of the            countries are described by the following Cobb– Douglas production functions:

North Economy: Y = AL.3K.7

South Economy: Y = AL.7K.3

a.   Which economy has the larger total production? Explain.

b.   In which economy is the marginal product of labor larger? Explain.

c.   In which economy is the real wage larger? Explain.

d.   In which economy is labor's share of income larger? Explain.

Answer:

a.   Output is the same in both economies, given the symmetry of the parameters of the production function and the equal quantities of labor and capital.

b.  The MPL is larger in the South Economy. The MPL depends on the value of (1 –α) and  the average productivity of labor (Y/L). Since the average productivity of labor is the     same in both countries, differences in the MPL depend on the value of (1 – α), which is larger in South Economy (.7) than in North Economy (.3).

c.   Since factors are paid according to the values of their marginal products, the real wage is larger in South Economy, because the MPL is larger in South Economy than in North Economy [from part (b)].

d.   Labor's share of income equals (1 – α), which is larger in South Economy (.7) than in North Economy (.3).

Question 4 (15 points)

Economists occasionally speak of "helicopter money" as a shorthand approach to             explaining increases in the money supply. Suppose the chair of the Federal Reserve flies  over the country in a helicopter, dropping 10,000,000 newly printed $100 bills (a total of $1 billion). By how much will the money supply increase in the following scenarios,       holding everything else constant:

a.   all of the new bills are held by the public as currency?

b.   all of the new bills are deposited in banks that choose to hold 10 percent of their deposits as reserves (and no one in the economy holds any currency)?

c.   all of the new bills are deposited in banks that practice 100-percent-reserve banking?

d.   people in the economy hold half of their money as currency and half as deposits, while banks choose to hold 10 percent of their deposits as reserves?

Answer:

a.   m =

b.  m =

cr + 1

=             = 1 → ΔM = m × ΔB = 1 × 1 = 1 billion

= 10 → ΔM = 10 × 1 = 10 billion

0 + 1

d.  m =             =       → ΔM ≈ 1.82 × 1 = 1.82 billion

or ΔM = 1 × 0.5 + 10 × 0.5 = 5.5 billion

Question 5 (5 points)

Do you agree no one is ex ante “not rational”? How about ex post? Explain.

Answer: Open! :)

Question 6 (15 points)

Assume that the demand for real money balance (M / P) is M / P = 0.6Y – 100i, where Y is national income, and i is the nominal interest rate (in percent). The real interest rate r is    fixed at 3 percent by the investment and saving functions. The expected inflation rate        equals the rate of nominal money growth. If Y is 1,000, M is 100, and the growth rate of   nominal money is 1 percent, what must i and P be?

Answer:

ΔV      ΔM     ΔY "expected inflation ... money growth"          ΔM

V       M       Y                   i.e. ΔY=ΔV=0                                     M

→ i = 几 + r = 1 + 3 = 4

→ M/P = 0.6Y − 100i = 0.6(1000) − 100(4) = 200 → P = M/200 = 100/200 = 1/2

Question 7 (5 points)

If 5 Swiss francs trade for $1, the U.S. price level equals $1 for a good, and the Swiss price level equals 2 francs for the same good. Calculate the real exchange rate between Swiss    goods and U.S. goods.

Answer: ε =  =  = 2.5

Question 8 (10 points)

Suppose a new technology is developed that increases investment demand. Holding other factors constant, will the quantity of investment spending increase more in a closed          economy or in a comparable small open economy? Explain. Assume that prices are          flexible and that factors of production are fully employed in both economies. Assume that there is perfect capital mobility for the small open economy.

Answer: Investment spending will not change in the closed economy but will increase in   the small open economy. In the closed economy, there is no change in domestic saving, so the domestic interest rate must rise to keep investment spending equal to the unchanged    domestic saving. In the small open economy, the increase in investment demand is            financed by net capital inflows (a decrease in net capital outflows) at the unchanged world interest rate. The decrease in net capital outflows raises the real exchange rate and reduces net exports in the small open economy.

Question 9 (10 points)

If the economy were at a steady-state unemployment rate with a separation rate of 0.02    per month and a job-finding rate of 0.10 per month, and the labor force were 100 million, how many individuals would lose their jobs each month?

Answer: U = L / (1 + f / s) = 100 / (1 + 0.1 / 0.02) = 16.7 million

E=100-16.7=83.3 million

Lost jobs=88.3 x 0.02 =1.67 million

Question 10 (20 points)

If the U.S. production function is Cobb– Douglas with capital share 0.3, and depreciation is 4 percent per year.

a.   To reach the Golden Rule steady state, what the saving rate must be?

b.   Given the previous part saving, solve for steady-state capital per worker, production per worker, and consumption per worker.

c.   Redo assuming a population growth of 3 percent per year.

Answer:

a.   Golden Rule: MPK = 6  0.3k −0.7 = 0.04 → k = () = ( ) Steady state: Δk = 0 → i = 6k → sf (k) = 6k → sk0.3 = 6k

→ s = 6k0.7 = 0.04(7.5) =  ×  =  ×  = 0.3

b.    → y = f(k) = (()) = ( ) ≈ 2.37  → c = (1 − s)f (k) = (1 − 0.3)(  15  ) ≈ 1.66