Iowa State University

Department of Economics

Intermediate Macroeconomics

ECON 302

Problem Set # 1  

Solutions

 1. Assume a simple economy with no government and no foreign sector. The model is:

TE = C + I

C = a + b Y

Where a = 100, b = .75, and I = 200.

a. Graph the consumption function using 4 values of Y.

Y
C
100
175
500
475
1000
850
1200
1000

 

b. In a separate diagram, graph the Total Expenditures schedule.

 

 

 

c. Calculate the equilibrium level of national product. What is the level of consumption at equilibrium Y?

Y = C + I

= a + bY + I

Y - bY = a + I

Y (1-b) = a + I

Y = (a+I)/(1-b)

Y*= (100+ 200) / (1 - .75) = 300 / .25 = 1200

 

when Y = 1200, C = 100 + .75 * 1200 = 1000

 

d. If actual output was 1000, what would the level of consumption be? What would the level of Total Expenditures be? Describe the process that would lead the economy back to equilibrium.

If Y = 1000, TE = C+I = 100 + .75 (1000) + 200 = 1050 > Y = 1000.

Thus, there is an excess demand for goods: an undesired decrease in inventories. Store managers would find their shelves emptying, which would cause them to call to their warehouses for deliveries. This would necessitate the warehouses making calls to factories to get their stocks back up. Factories would respond by increasing output.

 

2. The model is:

TE = C + I + G

C = a + b (Y - t Y + TR)

I = I

G=G

where
a = 60
G = 250
b = .8
TR = 200
t = .25
I = 200

a. What is the equilibrium level of national product?

Y = C+I+G

= a + b (Y - tY + TR) + I + G

= a + bTR + b (1 - t) Y + I + G

Y - b(1 - t) Y = a + bTR + I + G

Y ( 1 - b (1 - t)) = a + bTR + I + G

Y = {a + bTR + I + G} / { 1 - b (1 - t)}

Y = { 60 + .8 (200) + 200 + 250} / { 1 - .8 (1 - .25)}

Y = {670} / { 1 - .8 (.75)} = {670} / {1 - .6} = 670 / .4 = 1675

 

b. What is the government's budget surplus?

BS = tY - G - TR

= .25* 1675 - 250 - 200 = 418.75 - 450 = - 31.25

c. The government decides to increase the tax rate to balance the budget. Let the change in the tax rate be +.04 (i.e., D t = +.04). Calculate the D Y from this tax rate change. What is the new equilibrium level of Y? What is the budget surplus? Graphically depict the effect of this tax rate change on Total Expenditures.

Since the change in Y = -124.07, the new Y = Y0 + DY = 1675 - 124.07 = 1550.93

The Budget Surplus is:

BS = .29*(1550.93) - 250 - 200 = 449.77 - 450 = -0.23 (which is close enough for government work)