Question

1. You are a consultant to the government of Zambonia.

You have the following information:

(1) Y = C + I + G + X - M

(2) C = 75 + 0.6Yd

(3) I = 125

(4) G = 81

(5) T = - 40+.35Y (tax equation)

(6) Yd = Y – T

(7) P is fixed at 1.0.

Note the T has two components: a lump-sum component (- 40) that is autonomous and not related to the level of Y; and a component that is related to the level of Y. The -40 not related to income would be, for example, a tax rebate where the government sends each tax payer a check.

Suppose the president of Zambonia tells you her economist estimate the production function for Zambonia to be: Y = 1.1K .3L .7 and full employment K and L are 500 respectively.

f. What level of government spending is needed to get the economy to full employment?

g. The president tells you she is up for re-election and to ensure re-election she wants mail checks to all tax payers. How much will this cost the government?

h. Suppose velocity is constant at 5.045 and the money supply is 93. Given the information presented, can the central bank push the economy to full employment? How and why?

Answer 1

We have the following information

(2) C = 75 + 0.6Yd

(3) I = 125

(4) G = 81

(5) T = - 40+.35Y (tax equation)

(6) Yd = Y – T

(7) P is fixed at 1.0.

Find current equilibrium level of income

Y = C + I + G + X - M

Y = 75 + 0.6*(Y - (- 40+.35Y)) + 125 + 81

Y = 75 + 0.6Y + 24 - 0.21Y + 125 + 81

Y - 0.39Y = 305

Y = 500

Hence current equilibrium gdp is 500. Full employment GDP = Y = 1.1(500)^ 0.3*(500)^0 .7 = 550. Hence there is a GDP gap (negative) of 50.  

f. Find spending multiplier = 1/1-mpc(1-tax rate) = 1/1 - 0.6(1-0.35) = 1.6393. Hence required increase in G is 50/1.6393 = 30.5

g. The president tells you she is up for re-election and to ensure re-election she wants mail checks to all tax payers. How much will this cost the government?

We want use tax to eliminate the GDP gap so tax multiplier is -0.6/1 - 0.6(1-0.35) = -0.9836. Required amount of checks and the cost to the government = 50/0.9836 = 50.8333

h. Suppose velocity is constant at 5.045 and the money supply is 93. Given the information presented, can the central bank push the economy to full employment? How and why?

From the quantity theory we have p x y = m x v

1 x 550 = 93 x 5.045

The left side of the equation is 550 and the right side is 469.185 so the current money supply is not sufficient. Money supply has to be increased and this can be done by open market purchases of government securities, reduced reserve requirements and discount ratio.