Homework #6

 

1. In most of our analysis we assume that Pe is exogenous in the short run, and it moves in the medium run in case Pe is different from P. In our analysis of the time inconsistency problem associated with monetary policy, we have deviated from this somewhat.

 

Suppose the initial value of M is M1  and there is a higher value, M2 > M1 .  Consider the plan, x=(M= M2 in short run, and M= M1 in medium run), y=( M= M1 ) forever after. This gives a short run jolt to the economy, without resulting in a permanent increase in the price level which, for reasons not in the model, is costly. This is an optimal plan from the perspective of a monetary authority who views the natural rate of output as being too small. Of course, the monetary authority would like to raise output permanently, but that’s not an option in our model.

 

This plan turns out not to be time consistent. To see this, suppose the monetary authority decides at some point to implement the plan, x, y, y, y….. . Then, the economy experiences a short run expansion, without a medium run rise in the price level. In the next period when y is to be implemented, suppose the monetary authority rethinks its plan (this is not unlike the US monetary authority, which rethinks its optimal plan each time that it meets). Note that the position of the monetary authority is the same now as it was in the previous period, when it chose to commit itself to x,y,y,… .

 

Explain why the optimal plan is not time consistent.

 

Suppose that monetary policy ends up doing x,x,x, … . Note that we now have a sequence of medium run equilibria. Explain why on average across this sequence of equilibria, the price level is higher. Eventually, people can be expected to notice that on average the price level is higher. Suppose that Pe rises.

 

Carefully work through the implications for the short and the medium run, of a rise in Pe . Explain how the rise confronts the monetary authority (especially one that worries a lot about the natural rate of output being too low) with a dilemma: accommodate the rise in expectations and prevent a recession, but at the cost of higher prices; or don’t accommodate at the cost of a recession, but no change in the price level.

 

Explain how the monetary authority who worries about the natural rate being too low, will be led to raise the money supply by more than what is implied in x, after Pe  is raised. Explain how this process of Pe  rising, followed by greater increases in M can lead to a perpetual rise in the price level, something we call inflation.

 

2. Suppose there is an increase in G in the AD-AS model. Run through the short and medium run analysis of this shock. Show the impact on output, interest rate, price level, unemployment in the short and the medium run. Now, suppose that the increase in Pe that occurs in the medium run, actually occurs instantly with the initial rise in G. What is the effect on output, interest rate, price level, unemployment in the short and the medium run.  In the light of your analysis, discuss the role of expectations in the speed with which the economy adjusts to a shock. In our discussion of the Lucas critique we explored another example where expectations matter for the impact of a shock (in that case, a change in the tax rate). Compare and contrast the way expectations matter in the example discussed here and the Lucas critique example.

 

3. Exchange rates move a lot. Suppose you are a Japanese car maker. It costs you 2 million Yen to make a car in Japan. Your owners require μ=10 percent return on costs, so you need to get 2.2 million Yen on the sale of a car. You sell your cars in the US. Suppose the exchange rate is as it was in 1985, i.e., (1/250) dollars per Yen. How much do you have to charge for your car in US dollars? In 1988 the dollar depreciated a huge amount, to (1/124) dollars per Yen. How much would you have to charge in US dollars in order to get the Yen you need to pay your costs and profits? Suppose you thought that such a price hike would cause you to lose all market share, and you decide not to change your US price, despite the US dollar depreciation. Compute the rate of return that you would be able to give your owners in this case (note: this will be a negative number).