know that national saving is 750, so we just need to set it equal to investment:
S = I 750 = 1,000 – 50r Solving this equation for r, we find:
r = 5%.
c. When the government increases its spending, private saving remains the same as before (notice that
G does not appear in the Sprivate above) while government saving decreases. Putting the new G into the
equations above:
Sprivate= 750 Spublic = T – G = 1,000 – 1,250= –250. Thus,
S = Sprivate + Spublic
= 750 + (–250) = 500.
d. Once again the equilibrium interest rate clears the market for loanable funds:
S = I 500 = 1,000 – 50r Solving this equation for r, we find: r = 10%.
Chapter 4
PROBLEMSAND APPLICATION:2
2.In the country of Wiknam, the velocity of money is constant. Real GDP grows by 5 percent per year, the money stock grows by 14 percent per year, and the nominal interest rate is 11 percent. What is the real interest rate?
The real interest rate is the difference between the nominal interest rate and the inflation rate. The
nominal interest rate is 11 percent, but we need to solve for the inflation rate. We do this with the quantity equation expressed in percentage-change form:
% Change in M + % Change in V = % Change in P + % Change in Y. Rearranging this equation tells us that the inflation rate is given by: % Change in P = % Change in M + % Change in V – % Change in Y. Substituting the numbers given in the problem, we thus find: % Change in P = 14% + 0% – 5%= 9%.
Thus, the real interest rate is 2 percent: the nominal interest rate of 11 percent minus the inflation rate of 9 percent.
Chapter 7
PROBLEMS AND APPLICATION:1（a,b,c）,3(a,b)
1.Country A and country B both have the production function Y = F(K, L) = K1/2L1/2. a. Does this production function have constant returns to scale? Explain. b. What is the per-worker production function, y = f(k)?
c. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using
your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state
levels of income per worker and consumption per worker.
3.Consider an economy described by the production function: Y = F(K, L) = K0.3L0.7. a. What is the per-worker production function?
b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.
Chapter 8
PROBLEMS AND APPLICATION:1
1.An economy described by the Solow growth model has the following production function:
y =√k.
a. Solve for the steady-state value of y as a function of s, n, g, and d.
b. A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A less developed country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g = 0.02 and d = 0.04. Find the steady-state value of y for each country.
c. What policies might the less developed country pursue to raise its level of income?
Chapter 10
PROBLEMS AND APPLICATION:2,5
2.In the Keynesian cross, assume that the consumption function is given by C = 200 + 0.75 (Y ? T ).
Planned investment is 100; government purchases and taxes are both 100. a. Graph planned expenditure as a function of income. b. What is the equilibrium level of income?
c. If government purchases increase to 125, what is the new equilibrium income? d. What level of government purchases is needed to achieve an income of 1,600?
a. Total planned expenditure is PE = C(Y – T) + I + G.
Plugging in the consumption function and the values for investment I, government purchases G, and taxes T given in the question, total planned expenditure PE is