economics

ECON 304 - Summer 2016 (Session I)

Homework 3

DUE: June 17th (FRIDAY), 2016

From the Syllabus:

1. Homework must be turned in on the day it is due. Late homework will NOT be

accepted.

2. You may work with your friends / classmates. However, you MUST put names of other

group members on your homework. You also MUST write up your own answers.

3. TYPE your work. Long equations and graphs may be hand-written.

4. BUY A STAPLER! (10% deduction from your homework grade if you do not staple

your homework)

5. Carefully explain your work! This means you MUST SHOW YOUR WORK FOR

YOUR CALCULATIONS.

6. Write your name! (Homework will not be graded if you do not put your name on your

homework.)

Name:

Course: ECON 304 (Summer I, 2016)

Group members (if any):

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Question 1

Consider the following model of the economy.

Production function:

Y = AKN − N2

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Marginal product of labor:

MPN = AK − N

where the initial values of A = 8, and K = 10.

The initial labor supply curve is given as:

Ns = 20 + 9w

Also, the desired consumption, desired investment, government purchases, and taxes are

given as:

Cd = 401 + 0.50(Y − T) − 500r

Id = 800 − 500r

G = 500

T = 100

and, the real demand for money is given as:

Md

P = 469 + 0.5Y − 1000r

and nominal supply is Ms = 4000.

We assume that expected inflation rate is zero (πe = 0) so that money demand depends

directly on the real interest rate (so i = r).

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(a) Solve for the labor market clearing real wage (w∗), the profit maximizing level of labor

input (N∗), and the full employment level of output (Y ∗). Please show your work.

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(b) Draw two diagrams vertically with the labor market on the bottom graph and the

production function on the top graph. Be sure to label everything including this initial

equilibrium point as point A.

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(c) Derive an expression for the IS curve (r in terms of Y). Please show your work.

(d) Find the real interest rate that clears the goods market. Please show your work.

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(e) Find the price level needed to clear the money market. Please show your work.

(f) Find the expression for the LM curve (r in terms of Y). Please show your work.

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(g) Now draw four separate diagrams.

• Top left: a desired savings equals desired investment

• Top right: a FE-IS-LM diagram

• Bottom left: a money market diagram

• Bottom right: An AD-AS diagram, locating this initial equilibrium point as point A.

Be sure to LABEL all diagrams .

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Question 2

How does each of the following factors affect the LM curve? Start your argument from

the diagram of MD-MS (money demand-money supply) and show how the associated change

will affect LM curve.

(a) An increase in nominal money supply.

(b) An increase in the risk of non-monetary assets relative to the risk of holding money.

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Question 3

How does each of the following factors affect the IS curve? Start your argument from the

diagram of Id − Sd and show how the associated change will affect IS curve.

(a) An increase in government purchases

(b) An increase in marginal productivity of capital.

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