Question

1. (The IS-LM-PC model): Assume the following relations characterize the goods market: (i) 1128 +0.2Y 300(rt + xt) (iii)G,-215 :T t = 200 (iv)st= 0.15 or 15% e) Derive the IS curve (as a relation between Y and r). (b) Assume the LM curve is given by r 0.16 (ie. in period t, the central bank sets the real interest rate at 16%). What is the short-run equilibrium level of output (Yt )? (c) Suppose that L = 2000 and un-0.07 (where L: labor force, un-natural rate of unemployment). Calculate the value of potential output (Ya). How does Yn compare to the short-run equilibrium level of output (Y)P (d) Calculate the natural rate of interest (rn). How does fm compare to r? How does Yn compare to the short-run equilibrium level of outputY) (e) What is occurring in this case: Inflation, Deflation, or Disinflation?

Answer 1

Solution:

(a) Deriving the IS curve:

Yt = Ct + It + Gt

Using the given information, and that disposable income, YDt = Yt - Tt (income net of taxes), this becomes:

Yt = 180 + 0.65(Yt - 200) + 128 + 0.2Yt - 300(rt + 0.15) + 215

Yt(1 - 0.65 - 0.2) = (180 -0.65*200 + 128 - 300*0.15 + 215) - 300rt

0.15*Yt = 348 - 300rt

OR Yt = 2320 - 2000rt

(b) With rt = 0.16, Yt = 2320 - 2000*0.16

Yt = 2320 - 320 = 2000

So, short run equilibrium level of output level is $2,000

(c) Since, number of unemployed, U = labor force*unemployment rate, here

U = 2000*0.07 = 140

So, number of employed people, E = 2000 - 140 = 1860

Since, nothing is mentioned of the production function, we assume each labor produces 1 unit of output with wage normalized, so natural level of output is 1860

Yn is clearly smaller than Yt, Yt - Yn = 2000 - 1860 = 140

(d) Natural rate of interest can be found by substituting natural rate of output in the IS curve

So, 1860 = 2320 - 2000*rn

rn = (2320 - 1860)/2000 = 0.23

So, natural rate of interest is 23%, which is higher than the short term interest rate of 16%.

(e)