Question

Y=Ybar=6000, G=1200.

C^d=3600-2000r+0.1Y

I^d=1200-4000r

Answer the following questions

a). What is S^d? (a function of r)

b). What is r at equilibrium?

c). Draw our results in b) in a graph.

d). What is r at equilibrium if G increases to 1500?

e). What is r at equilibrium if G decreases to 1000?

Answer 1

(a) National Saving (Sd) = Y - C - G
=> Sd = 6000 - (3600 - 2000r +0.1Y) - 1200

=> Sd = 6000 - 3600 + 2000r -0.1(6000) -1200

=> Sd = 1200 + 2000r - 600

=> Sd = 600 + 2000r

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(b) At goods market equilibrium; Sd = I

=> 600 + 2000r = 1200 - 4000r

=> 2000r + 4000r = 1200 - 600

=> 6000r = 600

=> r = (600 / 6000)

=> r = 0.1

Equilibrium r is 0.1

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(c)

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(d)

National Saving (Sd) = Y - C - G

G increases to 1500
=> Sd = 6000 - (3600 - 2000r +0.1Y) - 1500

=> Sd = 6000 - 3600 + 2000r -0.1(6000) -1500

=> Sd = 900+ 2000r - 600

=> Sd = 300 + 2000r

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At goods market equilibrium; Sd = I

=> 300+ 2000r = 1200 - 4000r

=> 2000r + 4000r = 1200 - 300

=> 6000r = 900

=> r = (900 / 6000)

=> r = 0.15

Equilibrium r is 0.15

The equilibrium interest rate will increase to 0.15

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(e)

National Saving (Sd) = Y - C - G

G decreases to 1000
=> Sd = 6000 - (3600 - 2000r +0.1Y) - 1000

=> Sd = 6000 - 3600 + 2000r -0.1(6000) -1000

=> Sd = 1400+ 2000r - 600

=> Sd = 800 + 2000r

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At goods market equilibrium; Sd = I

=> 800 + 2000r = 1200 - 4000r

=> 2000r + 4000r = 1200 - 800

=> 6000r = 400

=> r = (400 / 6000)

=> r = 0.067

Equilibrium r is 0.067

The equilibrium interest rate will decease to 0.067

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