of University Waterloo Department of Economics ECON 202 001 w07 Assignment # 2, SOLUTIONS
Answer all of the following questions. Show your work for full marks.
1. Varied (4) 2. Suppose that the economy of Briarwood has the following characteristics: AD: Y=900 + M/P SRAS: Y=Y + 10(P-Pe) and Y=1000 and u=0.05 a. If Briarwood is in long run equilibrium at M=500 and P=Pe, what is P? (2) In long run eq'm, Y=1000, so 1000=900 + 500/P 100=500/P P=5 b. Suppose that the government announces an increase in M to 550, but they actually increase M to 650. If Okun's law holds in Briarwood, what are the short run values of Y, Pe and u? (4) Expected SRAS will intersect LRAS at expected AD line. 1000=900+ 550/P --> P=5.5 So expected price is 5.5 and SRAS: Y=1000+10(P-5.5) but actual AD is: AD: Y=900 + 650/P In short run, we are at intersection of SRAS and AD curves. Set equal and solve for P, then plug P in and solve for Y. 900 + 650/P = 1000+10(P-5.5) 0 = 100 -650/P +10P 55 0 = -650 + 45P + 10P2 Solve using quadratic formula: P= -45 + or 452 -4(-650)(10) 2*10
The solutions is : 6.12 or -10.62, but because we know that the short run price must be higher than 5.5 and lower than 6.5 (see graph below), then we know the solution is 6.12.
AD-AS Misperceptions P
LRAS SRAS(Pe=5.5)
6.5 6.12 5.5 5
SRAS(Pe=5) SR AD(M=650) E1 AD(M=550) AD(M=500)
1000
1006.21
Y
To solve for Y, we plug 6.12 into our AD or SRAS curve: Y=900 + 650/6.12 = 1006.21 To solve for u, we use okun's law: a 1% fall in u from u leads to a 2% increase in Y over FE. Now output has increased by (1006.21-1000)/1000 = .00621, so we know that unemployment must have fallen by .00621/2 or .0031 So u=.0469 Mathematically Okun's law is: (Y-Y)/Y =-2(u-u) c. Given the above, find the expectations augmented Phillips curve slope. (2) The Phillips curve is: - e = -h(u-u) We have u and u, so to determine the slope, -h, we need to solve for and e. Recall: = P/P, We have both expected and actual price changes, so = (6.12-5)/5 = .224 & e= (5.5-5)/5 = .1 .224 - .1 = -h(-.0031) -h = -40
3. The closed economy of Wawel is in long-run (general) equilibrium, with =0.02 and a natural rate of unemployment of seven percent. Assume that Okun's law holds and let the expectations augmented Phillips curve be: _ = e -2(u-u) Suppose that the King of Wawel embarks on a program to reduce unemployment over a period of three years. In the first year, he will reduce the unemployment rate to 0.06, in the second year he will reduce it further to 0.05, and in the third he year will hold it constant at 0.05. Expected inflation is the inflation rate of the previous year. So in the first year of the King's program, expected inflation is .02. a. What is the actual inflation rate that the King must generate in order to reduce the unemployment rate in Wawel on schedule for each of the three years of the program? And what will be e for years 2 and 3? (4) _ = e -2(u-u) year 1, u=.06, e =.02, and natural rate of unemployment fixed at .07 = .02- 2(.06-.07) = .04 year 2, u=.05, e =.04, and natural rate of unemployment fixed at .07 = .04 - 2(.05-.07) = .08 year 3, u=.05, e =.08, and natural rate of unemployment fixed at .07 = .08 - 2(.05-.07) = .12 b. Relative to full-employment output, by what percent does GDP rise in the first, second and third years? (2) Recall that Okun's law is: (Y-Y)/Y =-2(u-u) So, in the first year, unemployment falls by 1%, so output rises by 2% in the second year, unemployment is 2% below the natural rate, so output is 4% above FE. (This represents a 2% increase from the first year) in the third year, unemployment is still 2% below the natural rate, so output is still 4% above FE. (This represents a 0% increase from the second year.
c. If you were hired to advise the King, what concerns might you raise about her program of reduced unemployment? (2) You might suggest that the costs of reducing unemployment are high and growing inflation levels. Inflation costs include shoe leather and menu costs. Note that even though the third year is simply ...