How much will the government have to print to raise

Reference no: EM133202762

Assignment:

1. Suppose an economy has maintained a constant zero-rate of money growth, µ_L = 0 as long as anyone can remember (...M_t-3 = M_t-2= M_t-1= M¯ ). As a result, they have never experienced inflation. Assume that the current price level, P_t-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:

v_t = 1 + i_t

(a) Suppose households have adaptive inflation expectations of the following form: E_t[π_t+1] = 1 2 π_t-1 + 1 2 π_t-2. Write inflation today, 1 + πt = P_t/P_t-1as 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 Y_g < 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 Y_g= 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¯ , Y_g, and velocity, v_t. What is velocity given that past inflation has been 0?

(d) Given your answer to part (c). What was inflation at time t, π_t? What are inflation expectations at t+1, E_t+1[π_t+2]?

(e) What is velocity at t+1? How much will the government have to ‘print' to raise another Y_g = 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 W_tfor 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) - ψL₁^1+γ/1 + γ + β (log(c₂) - ψL₂^1+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 Y_t equal to? Use this and the fact that Y_t = F(L_t) = L_t to solve for wages as a function of output, Y_t.

(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:

π_t= β₁(Yt - Y¯ ) + β₂(E[π_t+1]) + e_t

Suppose γ was very close to zero. Would we expect β₁to 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: π_t = β₁(u_t - u¯) + β₂E_t[π_t+1] + v_t

Where u_tis 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?

Reference no: EM133202762

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