Answer to Question #183698 in Macroeconomics for Jayla

Question

The following equations describe the economy.

• C = 100+ 0.8 Y

• I = 200- 1000 i

• L = Y – 10000 i

Initially, government expenditure is $550, and taxes are $500. The real money supply equals

$900.

a. Derive the formulas for the IS curve and LM curve. (4pts)

b. What are the initial levels of GDP, the interest rate, consumption, and investment?

Owing to a drop in investor confidence, the autonomous component of investment drops

by 90. (2pts)

c. By how much do income, the interest rate, and investment drop? (3pts)

d. By how much should the money supply be changed in order to return GDP to its original

level? What will the new interest rate be? (3pts)

e. Draw three graphs to illustrate the equilibria in b, c, and d. (6pts)

Answer 1

a. The formulas for the IS curve and LM curve are:

IS: Y = C + I = 100 + 0.8Y + 200 - 1000i,

0.2Y = 300 - 1000i,

Y = 1500 - 5000i.

LM: Ms = Md, so:

Y – 10000i = 900,

Y = 900 + 10000i.

b. The initial levels of GDP, the interest rate, consumption, and investment are:

1500 - 5000i = 900 + 10000i,

15000i = 600,

i = 0.04,

Y = 900 + 10000×0.04 = 1300.

C = 100 + 0.8×1300 = 1140,

I = 200 - 1000×0.04 = 160.

c. If the autonomous component of investment drops by 90, then income, the interest rate, and investment will decrease.

d. The money supply should be decreased in order to return GDP to its original. The new interest rate will be the same as before the change.