Question

Suppose the goods market in an economy is represented by the following equations.
C = 500 + 0.5YD I = 500 – 2000 i + 0.1Y G = 500
X = 0.1Y* + 100e Q = 0.2Y - 100e T = 400
Y* = 1000 i = 0.05 (5%) e= 1
Z = C + I + G + X - eQ Y = Z (equilibrium condition)

a. Solve the model and find the equilibrium value for GDP (Y).
b. Given your answer in a, calculate C, I, X and Q.
c. At this level of output, is the economy experiencing a trade surplus or deficit?
d. Suppose G increases by 100 (to 600). Calculate the new equilibrium level of output. What is the size of the multiplier?
e. Based on your answer to d, calculate the new level of Q. Calculate the change in net exports caused by this increase in G.
f. Suppose the marginal propensity to imports (in imports equation) decreases from 0.2 to 0.1. Assume all other variables are the same. What happens to the size of multiplier? Compare the changes in Y caused by the increase in G in part d and with a new marginal propensity to imports (0.1).

Answer 1

a)$Y=500+0.5Y+500-2000×0.05+0.1Y+500+0.1×1000+100×1-0.2Y+100;$ $Y-0.5Y-0.1Y+0.2Y= 1700;$

$0.6Y=1700; Y=2833;$

b) $C=500+0.5*2833; C= 1916.5;$

$I=500-2000*0.05+0.1*2833; I=683.3;$

$X=0.1*2833+100; X=383.3;$ $Q=0.2*2833-100*1; Q=466.6;$

c) at the current level of production, the economy is experiencing a trade surplus because net exports are $383.3;

d) G$=600;$

$Y=500+0.5Y+500-2000×0.05+0.1Y+600+0.1×1000+100×1-0.2Y+100; 0.6Y=1800; Y= 3000;$

$e) X= 0.1*3000+100; X=400; Q= 0.2*3000-100; Q=500;$