5(a) The AD curve is given by equation (5.7); explicit values can be substituted into it.
By simplification we obtain the linear relationship:
The slope is -.757 and the vertical intercept is 1.865. [10]
5(b) First, y = ye = 2.33, the antilog of which is 10.278. Next, pi = mu = .10 or 10%. Finally, substitute know values into the LM equation: 1.71 = .75 x 2.33 - .25i or i = .15 or 15%. [10]
5(c) Because the growth rate of the money supply has not changed, pi and pie will remain at 10%; y will fall to 2.15. Then, substitute into the IS equation: 2.15 = 4 - 33.4(i - .10) and obtain i = .155 or 15.5%. The real interest rate is 5.5%. Real money balances fall to .75 x 2.15 - .25 x .155 = 1.574. [10]
5(d) The new AD equation becomes
or pi = 1.877 - .757 yd and the new AS equation becomes y = 1.28 + 7 pi, which solves for pi = .144 or 14.4% (higher) and y = 2.288 (lower). Then m - p = 1.71 + .10 - .144 = 1.666 (lower) amd from the IS equation, solve for i = .20 or 20% (higher). In this case, long-run properties cannot be invoked since mu did not rise to 15%. [10]
5(e) From the IS equation, we can write
or the real interest rate equals .065 or 6.5% (higher). The nominal interest rate is i = .065 + .10 = .165 or 16.5% (higher). [10]
1(a) First solve for the change in the inflation rate: Delta pi = [1/(1 - a3)] Delta mu = [1/(1 - .25)][5 - 10] = - 6.67%; so that pi = 3.33%. Since pi = pie, y will remain at 2.33. Also, i must fall by the same extent as the inflation rate to keep the real interest rate constant; this i = 15 - 6.67 = 8.33%. Finally (m - p) = (m - p)-1 + mu - pi = 1.71 + .05 - .033 = 1.727. [10]
1(b) This makes the reduction in the growth rate of the money supply into a monetary shock, with xm = -0.05. From equation (6.10), we know that Delta pi = [a1/(a1 + a3a4 + a2a2a4)][xm] = [33.4/(33.4 + .25 x 7 + 33.4 x .75 x 7)][-0.05] = 33.4/210.5 x - 0.05 = -0.79%, so that pi falls to 9.207%. Then substitute into the AS equation: y = 2.33 - 7(10 - 9.207)/100 = 2.274. Next substitute into the IS equation so that 2.274 = 4 - 33.4(i - .10) or i = 15.17% and i - pie = 15.15 - 10 = 5.17%. Finally, m - p = (m - p)-1 + mu + xm - pi = 1.71 + .10 - .05 - .092 = 1.668. [10]
1(c) Expectations of inflation will fall as in 1(a) above, namely pie = 3.33%. However, no other exogenous variable changes. Thus derive an AD equation from (6.5) and obtain
pi = .10 + 1.71 - [.75 + (.25/33.4)]yd + (.25 x 4)/33.4 + .25 x .033.
By simplification, the AD equation becomes pi = 1.8483 - 0.7575yd. The AS equation becomes y = 2.0969 + 7pi, which can be substituted into the AD equation: pi = 1.8483 - 0.7575(2.0969 + 7 pi) which solves for pi = 4.12%. Next from the AS equation, y = 2.33 - 7(3.33 - 4.12)/100 = 2.386 which is higher because expected inflation fell more than actual inflation. Also, from the IS equation, 2.386 = 4 - 33.4(i - .033), so that i = 8.16% and i - pie = 8.16 - 3.33 = 4.83%, which is lower as required to stimulate demand for the extra output. Finally (m - p = 1.71 + .10 - .0412 = 1.769. [10]
3. From the IS curve, write 2.35 = 4 - 33.4(.15 - 10) + xg which solves for xg = 0.02. Then, from the AS equation, we derive 2.35 = 2.33 - 7(.10 -.12 - xs) + xs, which solves for xs = -0.015. Finally, in the LM equation, we write .10 - .12 + xm = .75 x 2.35 - .25 x .15 - 1.71, which means that xm = 0.035. Therefore, there were positive shocks to the goods and money markets and a negative supply shock. [20]
5(a) Solve the following equation: 0.0333 = .016 + .01327(il - is) or il - is = 1.304% [10]
5(b) Equilibrium is attained when Delta is = 0 and the slope of the yield curve is constant over time. Thus il - is = .2755 - 0 + .7787(il - is) or il - is = 1.244%. [10]
5(c) Solve equation (6.23) and the yield curve. In the first year, il - is changes from 1.244% to 1.809%, but this steeper yield curve does not affect output in the same year, thus Delta y = .033. In the second year, il - is = 1.684 and Delta y = .04. In the third year, il - is = 1.587 and Delta y = .0384. [20]