Question

Suppose output is determined by

$Y=A\sqrt{k}\sqrt{L}$

where A represents technology levels, K is capital, and L is labor. Suppose that A=10, K=100, and L=25.

Demand for investment funds is given by

$I=100-1000*r$

where r is the interest rate.  (Note: If r is 5% than r=.05)

$C=400-1000*r$

Consumers save more (ie consume less) when the interest rate is high.  So consumption is given by

The government consumes G=100.

1. What is the level of output in this economy?

2. What is the equilibrium level of the interest rate?

3. How is output divided between C, I, and G at equilibrium?

4. How would your answers to parts a-c change if government consumption rose to 150?  In two sentences explain intuitively what is (and isn’t) going on as the government consumes more.

Answer 1

(a)

Output (Y) = 10 x $\dpi{80} \sqrt{}$ 100 x $\dpi{80} \sqrt{}$ 25 = 10 x 10 x 5 = 500

(b)

In equilibrium, Y = C + I + G

500 = 400 - 1000r + 100 - 1000r + 100

-100 = -2000r

2000r = 100

r = 0.05 (= 5%)

(c)

C = 400 - (1000 x 0.05) = 400 - 50 = 350

I = 100 - (1000 x 0.05) = 100 - 50 = 50

G = 100

(d)

Since equilibrium Y depends on A, K and L, increase in G will not change value of equilibrium output and Y remains 500.

When G = 150,

In equilibrium, Y = C + I + G

500 = 400 - 1000r + 100 - 1000r + 150

-150 = -2000r

2000r = 150

r = 0.075 (= 7.5%)

Interest rate will increase by 2.5% (= 7.5% - 5%).

C = 400 - (1000 x 0.075) = 400 - 75 = 325

Consumption will decrease by 25 (= 350 - 325).

I = 100 - (1000 x 0.075) = 100 - 75 = 25

Investment will decrease by 25 (= 50 - 25).

Intuitively, as government increases spending, it borrows more for financing the higher budget deficit which increases interest rate. Higher interest rate decreases both consumption and investment, keeping output unchanged.