In: Economics
Consider the following equations that describe desired consumption, desired saving, taxes, and the demand for money of a hypothetical economy.
Cd = 200+0.75(Y-T)-500r
Id = 250-500r
T= 20+0.4Y
Md/P = 0.5Y -250(r+πe)
The values of other variables are: Y=1000, G=200, πe = 0.1, the nominal money supply=10,000.
(a) Find the general equilibrium values of the real interest rate, consumption, investment, and price level.
(b) Find the size of government budget deficit or surplus?
(c) Derive the equation that describes the IS curve without substituting for Y (Hint: For any level of output, Y, find an equation that gives the real interest rate, r, that clears the goods market. This involves writing the goods market equilibrium condition and solving for r (as a function of Y and other variables).
(d) Derive the equation that describes the LM curve without substituting for Y (Hint: For any level of output, Y, find an equation that gives the real interest rate, r, that clears the asset market. This involves writing the goods market equilibrium condition and solving for r (as a function of Y and other variables).
(e) Describe what the effects of increasing G would be on the general values of the real interest rate, consumption, investment, and price level.
In an economy, at equilibrium, Y=AD, where Y is the level of output and AD, is the aggregate demand
AD= C(YD)+I+G
The components of AD is the consumption investment and government expenditure
AD = Cd + Id + G
Consider the following hypothetical economy.
AD = 200+0.75(Y-T)-500r + 250-500r + 200
= 200+0.75(Y-20-0.4Y)-500r + 250-500r + 200
= 200 +0.75Y -15 – 0.3Y -1000r +250 +200
= 635 + 0.45Y -1000r
At equilibrium, Y=AD
Y = 635 + 0.45Y -1000r
Y – 0.45Y = 635 -1000r
0.55Y = 635 – 1000r
Putting the value of Y we get,
0.55(1000) = 635 – 1000r
1000r = 635 – 550
r = 85/1000
r = 0.08
This is the general equilibrium values of rate of interest.
Cd = 200+0.75(Y-20-0.4Y)-500r
= 200 -15 +0.45Y – 500r
= 185 + 0.45(1000) – 500 (0.08)
= 185 +450 – 40
= 595
This is the the general equilibrium values of consumption.
Id = 250-500r
= 250 – 500(0.08)
= 250 – 40
= 210
This is the the general equilibrium values of the investment.
At money market equilibrium , MD = MS
Md/P = 0.5Y -250(r+πe)
MS = 10000
10000/P = 0.5Y -250(r+πe)
P = 10000/ [0.5(1000) – 250( 0.08 +0.1)]
= 10000/ [500-45]
= 10000/455
= 21.9 = 22(approx)
This is the the general equilibrium values of the price.
(b)
T= 20+0.4Y [ Y=1000 given]
= 20 + 0.4(1000)
= 20 +400
= 420
The size of government budget deficit = Government expenditure – government revenue (Tax)
= G – T
= 200 – 420
= -220
The negative value of government deficit means the government has budget surplus by the amount 220. The revenue of the govt is greater than the expenditure.
(c)
AD= C(YD)+I+G where C is a function of disposable income (Y-T)
AD = 200+0.75(Y-T)-500r + 250-500r + 200
= 200+0.75(Y-20-0.4Y)-500r + 250-500r + 200
= 200 +0.75Y -15 – 0.3Y -1000r +250 +200
= 635 + 0.45Y -1000r
At equilibrium Y=AD
Y = C(YD)+I+G
Y = 635 + 0.45Y -1000r
Y – 0.45Y = 635 -1000r
0.55Y = 635 – 1000r
1000r = 635 – 0.55Y
.r = 0.635 – 0.0005Y
This is the equation of the IS curve.
(d)
At money market equilibrium, MD = MS
Md/P = 0.5Y -250(r+πe)
MS = 10000
10000= 0.5Y -250(r+πe)
250(r + 0.1) = 0.5Y -10000
250r = 0.5Y- 10020.5
.r = 0.002Y – 40.082
This is equation of LM curve.
(e)
G is a component of AD curve. If G increases, it will affect the AD curve. The curve will shift upward because increasing G will affect the coefficient of the curve. Thus there is a shift in the IS curve. IS curve shifts to rightward as a result, the rate of interest and the level of output both increases.
Consumption will also rise.
Again investment is a function of rate of interest. There is a negative relation between the rate of interest and the investment. Increase in r implies fall in investment.
Increase in rate of interest induces to rise in price level P.