Homework 6-

1. Consider the following simple Keynesian model:

Y = C + S + T

C = 100 + 0.7(Y-T)

I = 200

G = 240

T = 0

The aggregate production function of the economy is

Y = 2*(L)^0.5.

The functions of demand for and supply of labor are:

Demand: (w/P) = 3000000-L

Supply: (w/P) = 2L

(a) Calculate the equilibrium output in this economy according to the Keynesian model.

(b) What is the equilibrium level of employment in this Keynesian equilibrium?  Is that different from the full employment level that is found by the intersection of the labor demand and supply functions? 

(c) Assume the government wants to move the economy to the full employment level of output by changing G.  What does G have to equal to reach the full employment level of output? 

(d) Graphically represent your answers in parts (a) through (c).  Hint: Draw two graphs vertically.  The upper graph should be the Keynesian Cross and the lower graph should be the "flipped" aggregate production function (with labor on the Y axis and output on the X axis).  Show the two levels of Y (equilibrium level and full employment level) and corresponding levels of L.

(e) Based on what you found in parts (a)-(d), explain the main difference between the Keynesian Model and the Classical Model (with special emphasis on roles of the government).

2.  Consider the following model. 

Y = C + S + T

AE = C + I + G + (X-M)

C = 260 + 0.8(Y-T)

T = 0.2*Y

G = 30

I = 50 - 2*r

M - X = 150

Md = 52 - .4*r

MS = 50

In the above equations, r is written as a percent.

(a) Find the equilibrium interest rate, investment, and output.

(b) Solve for the expenditure multiplier and the tax expenditure multiplier.

(c) What will happen to output if the government decides to achieve a balanced budget by changing G (i.e., they set G = T = 0.2Y).

3. For each of the following transactions, what is the effect (increase or decrease) on M1?  On M2?

(a) Jack sells a few shares of stock and put the proceeds into his savings account.

(b) A secret society burns $25 million.

(c) Mary sells a few shares of stock and put the proceeds into her checking account.

(d) Peter transfers money from his savings account to his checking account.

(e) The government prints $10 billion.

(f) Susie discovers $5 under the floor mat in her kitchen and deposits it in her checking account.

(g) Paul changes his travelers checks into cash and deposits it in his savings accounts.

(h) Jackie discovers $1 in her drawers and deposits it in her saving account.

4.  Assume that the government requires all Banks are required to hold $1 in reserves for every $10 of deposits.  Assume there are initially $0 in banks.

a) Suppose that Bratt deposits $2000 in cash in Bank SSC. Fill in the following table for Bank SSC immediately after Bratt has made his deposit.

b) Now suppose that Bank SSC lends out any excess reserves to Jonathan. Jonathan uses the entire loan to buy books from College Bookstore, who deposits his payment in Bank Ingraham. Fill in the following table for Bank SSC and Ingraham immediately after College Bookstore has deposited his payment (Jonathan's loan) in Bank Ingraham.

c) Suppose that Bank Ingraham lends out all of its excess reserves to Fabrizio, and Fabrizio's loan ends up being deposited in Bank Bascom. Fill in the following blanks.

d) Continuing this process infinitely, what is the total value of reserves, loans, and DD in this economy?  What will happen if the Fed increases the RR ratio to 20%?