Using Cagan model(appendix of chapter of mankiw book), derive the inflation rate. Just assume that we are in the perfect foresight world. If the money supply grwth rate is given by some constant, what is the inflation rate? Answer

Answer .
The equation for the demand for money is: Md = P * L(R,Y). This is the equivalent of stating that the nominal amount of money demanded (Md) equals the price level (P) times the liquidity preference function L(R,Y)–the amount of money held in easily convertible sources (cash, bank demand deposits). Among the most important variables that can shift the demand for money are the level of income and real GDP, the price level, expectations, transfer costs, and preferences. The overall level of prices in an economy adjusts to bring money supply and money demand into balance. When the central bank increases the supply of money, it causes the price level to rise. Persistent growth in the quantity of money supplied leads to continuing inflation. increases in the money supply in those countries isn’t associated with sustained increases in output that we would have predicted with monetary policy. It seems that in the short run, increases in the money supply lead to increases in output, but in the long run increases in the money supply just cause inflation.
4.(This problem requires the use of calculus.)Consider a Cobb–Douglas production functionwith three inputs. K is capital (the number ofmachines), L is labor (the number of workers),and H is human capital (the number of collegedegrees among the workers). The productionfunction is…..

Answer.

1. 
   Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor?
   

MPL = 1/3*K^1/3H^1/3 L^-2/3. Increase in human capital raises MPL.
b.Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital?
MPH = 1/3*K^1/3H^-2/3 L^1/3. Increase in human capital lowers MPH.
c.What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what share of total income do you think all workers would appear to receive?
1/3, 1/3, and 2/3, respectively.

d.Say an unskilled worker earns the marginal product of labor, whereas a skilled worker earns the marginal product of labor plus the marginal product of human capital. Using your answers to (a) and (b), find the ratio of the skilled wage to the unskilled wage. How dies an increase in the amount of human capital affect this ratio? Explain.
W_skilled/W_unskilled = (MPL + MPH) / MPL = 1 + (L/H). When H increases, this ratio falls because the diminishing returns to human capital lower its return, while at the same time increasing the marginal product of unskilled workers.

e.Some people advocate government funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate?
If more college scholarships increase H, then it does lead to a more egalitarian society. The policy lowers the returns to education, decreasing the gap between the wages of more and less educated workers. More importantly, the policy even raises the absolute wage of unskilled workers because their marginal product rises when the number of skilled workers rises.
5. . Consider an economy described by the following equations:Y = C + I + G
Y = 5,000, G = 1,000, T = 1,000, C = 250 + 0.75(Y − T), I = 1,000 − 50r.
b. Find the equilibrium interest rate.
c. Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving.
d. Find the new equilibrium interest rate.
Answer.
Consider an economy described by the following equations:Y = C + I + G
Y = 5,000, G = 1,000, T = 1,000, C = 250 + 0.75(Y − T), I = 1,000 − 50r.
a. In this economy, compute private savings, public savings, and national savings. Private Savings = Y – T – C = 5000 –1000 – (250 + .75(5000-1000)) = 750
Public Savings = T – G = 1000 – 1000 = 0.
National Savings = Y – C – G = 5000 – (250 + .75(5000-1000)) – 1000 = 750

b. Find the equilibrium interest rate (r).

750 = 1000 – 50r thus 50r = 250 and r =5.

c. Now suppose that G rises to 1,250. Compute private, public, and national savings?

National Savings = Y – C – G = 5000 – (250 + .75(5000-1000)) – 1250 = 500
Private Savings = Y – T – C = 5000 –1000 – (250 + .75(5000-1000)) = 750
Public Savings = T – G = 1000 – 1250 = -250.

d. What is the new equilibrium interest rate?

500 = 1000 – 50r thus r = 10.
Sukhrobbek Abdinazarov
320-RI