Question

1) Consider an economy in the short-run with the price level P fixed at 1 (P = 1). Other relevant information is: C = 100 + 0.75 * (Y – T) I = 750 – 20 * r T = -40 + (1/3)Y G = 1000; Y = C + I + G (M/P)d = 0.4 * Y – 48 * i M s = 1,200 (M/P)d = Ms /P Suppose investors and bond traders expect inflation, ?e = 0, so that i = r.

(a) Present a properly labeled IS-LM graph showing the equilibrium level of Y and r. Label this point A. (b) Solve for the new equilibrium the level of Y and r if G is increased by 200. And show this on your graph prepared in part (a). Label the new equilibrium point B. (c) Calculate ? Y/ ?G? Is it the same as 1-/(1-MPC+MPC(t)), If not, explain why? (d) Using a flow chart as I use in class, explain the dynamics of the transition from point A to B. Make sure to show the feedback effects. (e) Set G back at its original level of 1000 and now increase the money supply by 200. Solve for the new equilibrium values of Y and r. Label this on you IS-LM graph as point C. (f) Using a flow chart as I use in class, explain the dynamics of the transition from point A to point C. Make sure to show the feedback effects.

Answer 1

1. The IS curve will be relation between the output and the interest rate for which the goods market clears. Hence, it will be as , ie or or or .

The LM curve will be relation between the output and the interest rate for which the money market clears. Hence, it will be as , ie and since P=1 and i =r, we have or .

(a) The graph is as below.

At the equilibrium, which can be found by equating the IS and LM curves, the points will be and (percent).

(b) If G is increased by 200, the effect will be on the IS curve. The new IS curve will be as   or or or . The graph is as below.

The new equilibrium output will be and the equilibrium interest rate will be .

(c) Now, or .

Notice that the tax rate is 1/3. The government spending multiplier will be or or . Hence, it is not the same.

The mismatch is due to change in the interest rate. For a change in government multiplier of 200, the change in output is not 2 times 200, instead of the actual change 1.5 times 200, because the equilibrium interest rate also changes as well. If the interest rate would've been constant, the change in output would be indeed 400 not 300.

(d) The flow chart is not given. However, the transition occurs as

• Initial equilibrium : A.
• Excess supply of good is there due to increase in governement spending.
• Excess demand for money due to excess supply of goods.
• As money supply is constant, increase in interest rate, as demand for money has increased.
• New Equilibrium : B.

(e) The IS curve returns to . The money supply is increased by 200. The new LM curve can be found as   and since P=1 and i =r, we have or . The new equilibrium will be where the IS and LM will intersect, ie or . The equilibrium Y will be as or . The graph is as below.