Question

Consumption function: Cb(Y-To) hFo Investment function:gogiro Equilibrium condition: Y-C+I Go Note: since we are considering only the goods market, the interest rate is assumed to be exogenous. F is a measure of consumer confidence and is also exogenous, and b, h, go, g1 are all constants and have the signs indicated above. a. Solve for equilibrium output. (3 points) b. Show the impact of a change in consumer confidence on equilibrium output. (3 points) Then use the consumption function to determine the impact of a change in consumer confidence on equilibrium consumption. (3 points) c. What is the impact of a change in the exogenous interest rate on equilibrium income? (3 points) d. If b-0.8, what is the impact on equilibrium output of a $10 billion increase in (i) T, or (ii) G, or (iii) both G and T? (3 points)

Please answer part c and d

Answer 1

(c)

Y = C + I + G0

Y = b(Y - T0) + hF0 + g0 - g1r0 + G0

Y = bY - bT0 + hF0 + g0 - g1r0 + G0

(1 - b)Y = hF0 + g0 - g1r0 + G0 - bT0

Y = (hF0 + g0 - g1r0 + G0 - bT0) / (1 - b)

Impact of change in r0 on Y = dY/dr0 = -g1 / (1 - b)

Since g1 > 0 and 0 < b < 1,

(-g1) < 0 and (1 - b) > 0. Therefore

(dY/dr0) < 0.

As interest rate increases (decreases), output decreases (increases).

(d)

MPC = b = 0.8

(i) Tax multiplier = -b / (1 - b) = -0.8 / (1 - 0.8) = -0.8 / 0.2 = -4

When T increases by $10 billion, Y decreases by ($10 billion x 4) = $40 billion.

(ii) Government spending multiplier = 1 / (1 - b) = 1 / (1 - 0.8) = 1 / 0.2 = 5

When G increases by $10 billion, Y increases by ($10 billion x 5) = $50 billion.

(iii) When both T and G increases by $10 billion,

Net increase in Y = Decrease in Y due to increase in T + Increase in Y due to increase in G = $(-40 + 50) billion = $10 billion