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Desired consumption is Cd = 100 + 0.8Y - 500r - 0.5G, and desired investment is Id = 100 - 500r. Real money demand is Md/P = Y - 2000i. Other variables are πe = 0.05, G = 200, Y (Full output level) = 1000, and M = 2100. (a) Find the equilibrium values of the real interest rate, consumption, investment, and the price level. (b) Suppose the money supply increases to 2800. Find the equilibrium values of the real interest rate, consumption, investment, and the price level. (Assume that the expected inflation rate is unchanged.)

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Answer:

Under a) r=0.1;Id=50;Cd=750;P=7 b) P only changes and is now 9.33

Explanation:

a)  In a closed economy national savings are equal to investments or:

S d = I d = Y - Cd - G

Id = Y - 100 - 0.8*Y + 500*r - 0.5*G

100 - 500*r = 0.2*Y -100 + 500*r -0.5*G

200 - 1000*r = 0.2*1000 - 0.5*200=100

-1000*r=-100

r= 0.1

i = 0.15

Id = 100 -50 =50

Cd= 100 + 800 - 50 - 100=750

P = Md/Y-2000 i

P= 2100/1000 -300=7

b) If money supply increases to 2800, the price level would be:

P = 2800/Y - 2000*i = 2800/Y- 2000*(i-inflation)

However, since the variables determining real interest rate remained the same, r is also the same or 0.1 and i is 0.15. Consumption and investment remain the same, only price level changes or:

P=9.33  

The equilibrium rate of interest will be 0.10.

  • Desired consumption = Cd = 100 + 0.8Y - 500r - 0.5G
  • Desired investment = Id = 100 - 500r.
  • Real money demand = Md/P = Y - 2000i.
  • πe = 0.05
  • G = 200
  • Y = 1000
  • M = 2100.

In a closed economy, National Savings = Investments

Sd = Id = Y - Cd - G

100 - 500r = Y - 100 - 0.8Y + 500r + 0.5G - G

200 - 1,000r = 0.2Y - 0.5G

Since Y = 1,000 and G = 200

200 - 1,000r = 200 - 100

r = 0.10

Since i = r + πe

i = 0.1 + 0.05 = 0.15

Investment = 100 - (500*0.10 = 50

Consumption = 100 + 0.8*1000 - 500*0.1 - 0.5*200

= 100 + 800 - 50 - 100

= 750

Md/P = Y - 2000i = 1000 - 2000*0.15 = 700

Md = 700P

Md = M

So, 700P = 2,100

P = 2100/700 = 3

Now, when the money supply increases to 2800, P = MD/Y - 2,000i

P = 2,800/1000 - 2,000(i - inflation)

P = 2,800/800

P = 3.5

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