Reference no: EM133202762
Assignment:
1. Suppose an economy has maintained a constant zero-rate of money growth, µL = 0 as long as anyone can remember (...Mt-3 = Mt-2 = Mt-1 = M¯ ). As a result, they have never experienced inflation. Assume that the current price level, Pt-1 = 1, output is fixed at Y¯ every period, the real interest rate is fixed at ¯r, and velocity is a function of the nominal interest rate:
vt = 1 + it
(a) Suppose households have adaptive inflation expectations of the following form: Et[πt+1] = 1 2 πt-1 + 1 2 πt-2. Write inflation today, 1 + πt = Pt/Pt-1 as a function of past inflation.
(b) All of a sudden, the government finds itself unable to pay its debts or raise taxes. It decides to print new money to obtain Yg < Y¯ of real output.
Will money creation today (time t) have any affect on inflation expectations?
Therefore, will money creation today change velocity today? Will it have an effect on inflation today?
(c) Let M¯ = 100, Y¯ = 100, r = 0, and Yg = 20. How much will the government have to print in order to raise Yg of real output? HINT: solve for the new price level, Pnew as a function of M¯ , Y¯ , Yg, and velocity, vt. What is velocity given that past inflation has been 0?
(d) Given your answer to part (c). What was inflation at time t, πt? What are inflation expectations at t+1, Et+1[πt+2]?
(e) What is velocity at t+1? How much will the government have to ‘print' to raise another Yg = 20 of real output? Assume that Y¯ = 100, r = 0.
(f) Was the hyper-inflation this country experienced due only to the government printing currency? Explain.
2. Suppose Households' receive a wage Wt for every hour they work and can invest in a bond, b with interest rate i. Suppose further that utility over work and consumption during the two periods is given by:
log(c1) - ψL11+γ/1 + γ + β (log(c2) - ψL21+γ/1 + γ)
The household's lifetime budget constraint is:
P1c1(1 + i) + P2c2 = W1L1(1 + i) + W2L2
(a) Set up the household's Lagrangian and find their inter-temporal (Euler) equations and their intra-temporal (labor supply) conditions.
(b) There are no net-exports (the economy is closed), no government spending, and no capital. Therefore what is Yt equal to? Use this and the fact that Yt = F(Lt) = Lt to solve for wages as a function of output, Yt.
(c) Use (b) to solve for ∂Wt/∂Yt and give intuition for your expression.
(d) As γ gets very close to zero, do wages become more responsive or less responsive to output? HINT: Plug γ = 0 into the expression from (c).
(e) Recall that the Phillips Curve is given by:
πt = β1(Yt - Y¯ ) + β2(E[πt+1]) + et
Suppose γ was very close to zero. Would we expect β1 to be large or small? Explain intuitively.
3. This question is about alternate theories of the so called ‘flattening' of the Phillips curve. To answer this question, use the following form of the Phillips Curve: πt = β1(ut - u¯) + β2Et[πt+1] + vt
Where ut is unemployment in the United States. A flattening refers to the coefficient β1 getting smaller.
(a) What theory did Jorgensen and Lansing (2019) offer for the flattening of the Phillips of the curve (pretend you're explaining it to a journalist)?
(b) Suppose firms are employing more and more workers from abroad. Therefore, their marginal costs are made up of both domestic wages and international wages. How might this fact provide an alternative/complementary explanation for the flattening of the Phillips curve?