Question

x Problem set +2 - INTRMOT MAX Microsoft Word - PS232 sp18 X C Consider The Goods Market Mox u/bbcswebdav/pid-3641779-dt-content-rid-32308594 1/courses/ECON_1054_001_19F/PSX209232 au 19 pdf + 1. Consider first the goods market model with (exogenously given) constant investment Consumption is given by C = c +(Y-T) and T. 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= b + b Y-bi b. Solve for equilibrium output. At a given interest rate, is the effect of a change in autonomous spending bigger than what is was in part (a)? Why? (Assume + b < 1.) Next, write the LM relation as M/P = d.Y-di c. Solve for equilibrium output (Hint: Eliminate the interest rate from the IS and LM relations.) Derive the multiplier (the effect of a change of one unit in autonomous spending on output) O eO W9

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Answer 1

(Part a)

Goods market equilibrium condition: Y = C + I + G

Y = c0 + c1(Y - T) + I + G

Y = c0 + c1Y - c1T + I + G

(1 - c1)Y = (c0 - c1T + I + G)

Y = (c0 - c1T + I + G) / (1 - c1)

Multiplier = $\dpi{80} \partial$ Y/$\dpi{80} \partial$(c0 + I + G) = 1 / (1 - c1)

(Part b)

Investment is an inversely related function of interest rate and directly related function of income.

In new goods market equilibrium condition:

Y = c0 + c1(Y - T) + b0 + b1Y - b2i + G

Y = c0 + c1Y - c1T + b0 + b1Y - b2i + G

(1 - b1 - c1)Y = (c0 - c1T + b0 - b2i + G)

Y = (c0 - c1T + b0 - b2i + G) / (1 - b1 - c1)

Multiplier = $\dpi{80} \partial$ Y/$\dpi{80} \partial$(c0 + b0 - b2i + G) = 1 / (1 - b1 - c1)

By given conditions, 1 > b1 > 0 and 1 > c1 > 0, so

(b1 + c1) < 1

Hence

(1 - b1 - c1) < (1 - c1)

Thus the increase in output from a given change in autonomous spending is lower when investment is a function of both interest rate and income.

(Part c)

(i) Using the goods market equilibrium condition,

Y = (c0 - c1T + b0 - b2i + G) / (1 - b1 - c1)..........(A)

Money market equilibrium condition: M/P = M0 = d1Y - d2i  [here M0: Constant/fixed Money supply]

d2i = d1Y - M0

i = [d1Y - M0] / d2

Plugging into (A) above,

Y = [c0 - c1T + b0 - b2 x {[d1Y - M0] / d2} + G] / (1 - b1 - c1)

Y = [c0d2 - c1d2T + b0d2 - b2d1Y + b2 x M0] / (d2 - b1d2 - c1d2)

Y + [(b2d1 / (d2 - b1d2 - c1d2)] x Y = [c0d2 - c1d2T + b0d2 + b2 x M0] / (d2 - b1d2 - c1d2)

[(d2 - b1d2 - c1d2 + b2d1) / (d2 - b1d2 - c1d2)] x Y = [c0d2 - c1d2T + b0d2 + b2 x M0] / (d2 - b1d2 - c1d2)

(d2 - b1d2 - c1d2 + b2d1) x Y = c0d2 - c1d2T + b0d2 + b2 x M0

Y = [c0d2 - c1d2T + b0d2 + b2 x M0] / (d2 - b1d2 - c1d2 + b2d1)

Multiplier = $//img.homeworklib.com/questions/286d77b0-f927-11e9-ac53-a368b95aaada.png?x-oss-process=image/resize,w_560$Y/$//img.homeworklib.com/questions/28cdd510-f927-11e9-850c-751c3aad1ce3.png?x-oss-process=image/resize,w_560$b0 = d2 / (d2 - b1d2 - c1d2 + b2d1)