Question

ca Question Two: Assume the following equations summarize the structure of an economy. с = C2 +0.7(Y-T) = 2,000 - 50 T = 150+ 0.15Y (M/P) = 0.3Y - 10r M/P = 3,000 = 2,000 -10r G 4,000 - 2y NX = 1,500 -0.1 Y-5r i A. Calculate the equilibrium real output (Y) and (r). B. If government spending increases by 100, compute by how much the fed must increase the money supply if it wants to avoid the crowding out of expansionary fiscal policy. Make sure to support your answer with the relevant graph. (20 points)

Answer 1

(a) The IS curve would be where or or or
Y = (2000 - 5r +0.7(Y - 150 - 0.15Y)) + (2000 – 10r) + (4000 -0.2Y) + (1500 -0.14 – 57)
or or or or . Equivalently, we have
T = 469.75 0.035257
.

The LM curve would be where or or
0.3} = 3000-10
or
= 10000 - 33.3333
. Equivalently, we have .

The equilirbium output would be at where the interest rate clears both goods and money market, which would be where or or or . The equilibrium interest rate would hence be or or .

(b) The increase in government spending by $\Delta G$ would mean that the intercept term of 4000 would increase by $\Delta G$ . We have the IS curve as or $Y = \frac{1}{1 - 0.295}(5395 - 20 r + G)$ or $\frac{\mathrm{d} Y}{\mathrm{d} G} = \frac{1}{1 - 0.295}$ , and since Y is linearly related to G, we have $g = \frac{\Delta Y}{\Delta G} = \frac{1}{1 - 0.295}$ or $g = \frac{\Delta Y}{\Delta G} = 1.4184$ . For $\Delta G = 100$ , we have $\frac{\Delta Y}{100} = 1.4184$ or $\Delta Y = 141.84$ , meaning that the IS curve would shift by 141.84. But due to increase in Y, the interest rate in the money market would increase, and would result to final increase in the equilibrium output less than the increase in the IS curve. This is known as crowding out effect.

In order for diffusing the crowding effect, the money supply can be increased so that the interest rate remains the same as before, so that there would be no crowding out effect. We have LM curve as $r = 0.03 Y - \frac{\overline M}{10}$ where M-bar is the money supply. For the output be increased to $Y + \Delta Y = 11796.9349 + 141.84$ or $Y + \Delta Y = 11938.7749$ , and the interest rate be same as before, we have $53.908 = 0.03 * 11938.7749 - \frac{\overline M}{10}$ or $\frac{\overline M}{10} = 358.163247 - 53.908$ or $\frac{\overline M}{10} = 304.255247$ or $\overline M = 3042.55247 \approx 3042.5525$ . Hence, money supply must be 3042.5525 for the interest rate to be the same after the increase in Y.

Hence, money supply must be increased by 42.5525 (= 3042.5525 - 3000) to avoid the crowding out effect.

The graph is as below.

80 r -70 IS' -60 IS LM -50 LM -40 1 + Y1) 13 Y 12400 30 11600 11000 112000 112200

The old IS and LM curves are labelled as IS and LM, while the new ones as IS' and LM'. For the IS curve shift to IS', the total increase in Y is from Y1 to Y3. But if money supply stays the same as LM, then due to crowding out, the equilibrium GDP would be Y2, for Y3 minus Y2 is the crowding out loss in GDP. However, for founded increased money supply, the LM curve would shift to LM' and the equilibrium GDP would increase to Y3, which is the full increase in GDP due to the increased government spending. Also note that in order to avoid the crowding out, the interest rate (the green line) must be same for the new IS-LM equilibrium.