Answer to Question #112286 in Macroeconomics for Kgothatso

Question

3.8Consider first the goods market model with constant investment that we saw in Chapter 3. Consumption is given by:
C = Co + c1(Y-T)
And I, G and T are given.
a. Solve for equilibrium output. What is the value of the multiplier? Now let investment depend on both sales and the interest rate: I=b0 +b1Y-b2i
b. Solve for equilibrium output using the methods learned in chapter 3. At a given interest rate, why is the effect of a change in autonomous spending bigger than what it was in part (a)? Why? (Assume c1 + b1 = 1)
MAE206D /April 2020
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c. Solve for equilibrium level of investment.
d. Let’s go behind the scene in the monetary market. Use the equilibrium in the money market M/P = d1Y – d2i to solve for the equilibrium level of the real money supply.
How does the real money supply vary with government spending?

Answer 1

a. Y=C+I+G

Y=[1/(1-c1)][c0-c1T+I+G], and the multiplier is equal to [1/(1-c1)]

b. Y= C0 + c1(Y-T) +b0 + b1Y-b2i+G

Y=C0+c1Y+c1T+b0 + b1Y-b2i+G

Y=C0+c1Y+c1Yd+b0 + b1Y-b2i+G

Y-c1Y-b1Y=C0+c1Yd+b0-b2i+G

Y(1-c1-b1)=C0+c1Yd+b0-b2i+G

Y=[1/(1-c1-b1)][c0-c1T+b0-b2i+G], and the multiplier is equal to [1/(1-c1-b1)].

 multiplier=1/1-c1-b1

consumption increases together with autonomous expenditures, since these expenditures are essentially your basic living expenses.Higher consumption leads to higher output Y (more things are being consumed/bought/built). Higher Y leads to higher investment I according to the given formula I = b0 + b1Y − b2i

c.Y-c1Y-b1Y=C0+c1Yd+b0-b2i+G

Y-c1Y-b1Y-C0-c1Yd-G-b0=b2i

Y(1-c1-b1)-C0-c1Yd-G-b0=b2i

i=[Y(1-c1-b1)-C0-c1Yd-G-b0]/b2

d. M/P=Y/V

d1Y - d2i=Y/V

with increasing government spending, nominal money supply increases, while real money decreases as a result of inflation