This is a Pset. The course is Money and Banking. I posted the Pset (word doc file) and also the...

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This is a Pset. The course is Money and Banking. I posted the Pset (word doc file) and also the class material (pdf) that is required to solve this question.Unit 2: Monetary Policy Optimal Monetary Policy Unit 2: Monetary Policy May, 31 2022 37 / 59 How does the Fed choose an it? We’ve discussed (1) how the Fed controls it and (2) how it affects spending and prices. But what does the Fed actually hope to achieve? When thinking about what interest rate policy to set, the Fed takes into account its duel mandate: 1 ‘Full’ employment 2 Stable prices (low steady inflation) Let’s go back to our New Keynesian model from the last unit, to see how a shock (i.e. a recession) plays out, and what monetary policy can do about the shock, and how the Fed weighs its two goals. Unit 2: Monetary Policy May, 31 2022 38 / 59 The NK model revisited We’ll make two adjustments to the NK presented in the previous unit: 1 3 periods instead of 2 (t ∈ (1, 2, 3)) 2 Downwardly rigid wages (nominal wages can never go down) The first change will allow to add a ‘medium run’ period. The second change will give us unemployment (why?) and let us study the concept of potential output. Potential output: the level of output such that all of the economy’s resources (in our case, all workers) are put to full use and there is no inflation. Unit 2: Monetary Policy May, 31 2022 39 / 59 Households Remember that households worked for the firm every period, earning wage Wt , and were able to save in a bond, bt . On the homework, you’ll solve the household’s optimization problem in 3 periods and show that they now have: 3 intra-temporal conditions instead of 2 2 Euler equations instead of 1 c−σt = Pt Pt+1 βt+1(1 + i)c −σ t+1 Note that the β terms now have a time subscript. This means they can change over time. If there are only 3 periods, how much will the household save in the last period? Then what will they consume? c3P3 = W3 Unit 2: Monetary Policy May, 31 2022 40 / 59 Firms Remember that y jt = L j t and that firms set their prices according to the following equation: Pt = ( ϵ 1− ϵ ) E [MCt ] = ( ϵ 1− ϵ ) E [Wt ] A fraction α of the firms know the true marginal cost so E [MCt ] = Wt , while (1− α) have to base their price off of their backward looking expectations, E [MCt ] = Wt−1. Question: If nominal wages (Wt) never go down, will there ever be deflation in this model? Finally, remember that when we derived this relationship, we used the fact that demand for the output of each firm, y jt was a negative function of their price, p (law of demand). Unit 2: Monetary Policy May, 31 2022 41 / 59 Central Bank Finally, remember that we had a central bank that can set the nominal interest rate, it . We’ll show that the Central Bank can achieve its policy goals by following a Taylor Rule of the form (ϕy and ϕπ are both positive): it = ī + ϕy (Yt − Ȳ ) + ϕπ(πt) Where Ȳ is ‘potential output’ and Y − Ȳ is the ‘output gap’. Unit 2: Monetary Policy May, 31 2022 42 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1? c−σ1 = P1 P2 β2(1 + i1)c −σ 2 Consumers demand less stuff today at current prices. Can firms lower their prices? No! Wages can’t fall, so firms keep prices constant, P1 = P0 and just produce less, Y1 = c1. How much labor do they demand then? LD1 = Y1 = c1 Do workers want to work less? Recall that the first-period intra-temporal (labor supply) condition is: c−σ1 W1 = L γ 1 No! If anything they want to work more. LS1 = (W1/c σ 1 ) 1 γ  Unit 2: Monetary Policy May, 31 2022 43 / 59 Potential output and the ‘output gap’ We just saw that when a β shock causes demand to fall, downwardly rigid nominal wages means that the amount of labor demanded is less than the amount that workers are willing to supply at that wage. Therefore we do not have full employment. Question: could firms employ more labor and therefore produce more without raising prices? Yes! How do we know this? Right now, LS(W1)− LD(W1) > 0, so firms could easily induce more workers to work for them without needing to raise wages (and thus prices). Therefore are we above or below potential output? Is the output gap positive or negative? Below full employment = output lower than potential = negative output gap Unit 2: Monetary Policy May, 31 2022 44 / 59 How should the Fed respond? The Fed has a mandate to maintain full employment and stable prices? Has there been any inflation or deflation? Nope! What about less-than-full employment? Remember our Taylor Rule: i1 = ī + ϕy (Y1 − Ȳ ) + ϕπ(π1) So the Fed should unambiguously decrease the interest rate, i1 until c1 (which equals Y1, which equals L D 1 equals labor supplied at the given (stuck) nominal wage, W1. LS1 = (W1/c σ 1 ) 1 γ = LD1 = c1 Let call this interest rate, iL Unit 2: Monetary Policy May, 31 2022 45 / 59 The economy starts to recover... Suppose that the panic that caused β2 to jump up subsides, and β3 falls to its ‘normal’ level. Suppose further that the Fed had yet to change , i2 which was still equal to iL. c−σ2 = P2 P3 β3(1 + iL)c −σ 3 Intuitively, iL was low enough to get c1 back to potential output with the higher β2. If iL is combined with β3 instead, do we expect c2 = Y2 will equal or exceed potential? Exceed! Y2 > Ȳ . How will firms get workers to produce this extra output, Y2? W2 = (C 1−σγ 1 ) γ Unit 2: Monetary Policy May, 31 2022 46 / 59 Inflation For the α flexible price firms, PF2 = ϵ 1−ϵW2 while the (1− α) sticky price firms still have the lower price:PS1 = ϵ 1−ϵW1, so: P2 = ( ϵ 1−ϵ )(αW2 + (1− α)W1) > P1 So what should the Fed do? How are they doing on full employment? How about price stability? i2 = ī + ϕy (Y2 − Ȳ ) + ϕπ(π2) They should increase i2! Unit 2: Monetary Policy May, 31 2022 47 / 59 Zero Lower Bound and Forward Guidance Unit 2: Monetary Policy May, 31 2022 48 / 59 Taking stock Thus far we’ve learned: 1 How the Fed controls interest rates 2 How interest rates affect spending and inflation 3 What interest rate the Fed wants to set Recap: a fixed Wt implies a given potential output (when labor supply=labor demand at the given wage): (Wt/c σ t ) 1 γ = ct . The Fed wants to achieve this level of output. What happens when spending falls low enough that the interest rate the Fed would like to choose is negative? Can interest rates be negative? Unit 2: Monetary Policy May, 31 2022 49 / 59 The ILB If your bank tried to charge you to keep your money in the bank, you’d just take out cash! It’s possible that you’ll tolerate a slightly negative rate, but there is definitely a interest rate lower bound (ILB). Suppose β jumps high enough such that:( c−σt+1β Pt Pt+1 (1 + iILB) )− 1σ = ct

Komalavalli · Accepted Answer

1.
a.
Under full employment labour supply L1S=(W1/c1σ)1/γ= LD=c1 ----------------(1)
When Yt =Lt, ct=Yt
Labour demand LtD= ct=Yt
Therefore Labour demand equals consumption at time t.
The level of consumption /output is derived by utilizing equation 1
We get consumption / output c1=Y1=(W1/c1σ)1/γ
W1 /P1 = 0.9
P1 = 1
W1/1 =0.9
W1 = 0.9
σ =0.5
γ=1
c1 = (0.9/c10.5)1/1
c1 = 0.9/c10.5
c1*c10.5 = 0.9
c11.5=0.9
c1 = (0.9)1/1.5
c1 = (0.9)0.67
c1 =0.

Unit 2: Monetary Policy Optimal Monetary Policy Unit 2: Monetary Policy May, XXXXXXXXXX / 59 How does the Fed choose an it? We’ve discussed (1) how the Fed controls it and (2) how it affects spending...

Answer To: Unit 2: Monetary Policy Optimal Monetary Policy Unit 2: Monetary Policy May, XXXXXXXXXX / 59 How...

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