Wednesday, February 25, 2015

Upward-Sloping Short-run Aggregate Supply

Today we add short-run aggregate supply (SRAS) to the analysis. The short-run aggregate supply curve is tricky to justify theoretically. Given an increase in the money supply, the SRAS convey that total output increases as a result of increase in aggregate demand and a delay in price adjustments. It is convenient to think of this in terms of nominal income and then consider the behavior of the individual variables.

Imagine that there is an increase in the money stock of 5%. Given the log-derivative of the equation of exchange, this looks like
%∆M + %∆V = %∆P + %∆y
Rewrite as:
%∆M + %∆V = %∆(Py)
For now, let’s assume that portfolio demand for money is constant. Now,
%5 + %0 = %∆(Py)
%∆(Py) = %5
Within a static model, we know that in the long-run, the price level will absorb the entirety of the change, and that y remains unchanged. This is known as the classical dichotomy. Often rendered, “Reals affect reals, and nominal affect nominal.” In the real world, however, we see that nominal changes have real effects. A more realistic rendition states, when the economic activity is in something close to an equilibrium condition, changes in nominal aggregates do not lead to long-lasting changes in a given measure of aggregate output. It is possible that at first a change in y comprises some portion of the change in the nominal income. In the long run, y returns to its original level as prices come to fully reflect the increase in the money stock.

A thought experiment is enough to convey the nature of short-run effects. Imagine that, over night, Hume’s money fairy has increased everyone’s money balances by exactly double. If, at the moment this occurred, not before, all agents became aware of this doubling, there would be no effect on the allocation and employment of resources. Now, let’s imagine that our agents only become aware of this slowly. Some agents are able to spend the money before prices rise. Of course some suppliers have become aware of this change, but certainly all of them have not. At least some of those who recognize their increase in cash balances will make purchasers from those suppliers who have not changed the price. These suppliers may even believe that there has been an increase in demand and will sell more than they would have if that had realized that they suffer from “money illusion.” This leads to a temporary increase in output that will last as long as suppliers do not increase their prices. Eventually, competition and a need for solvency forces them to act in accordance with economic reality. Prices rise and output falls back to its long-run level.

As prices rise, there is no reason to expect that all prices move in the same direction at the same time. It is possible that a substantial portion of the increase in money is used to purchase only one or a few types of goods. These markets receiving the new money will increase prices more quickly than those that do not. For example, the doubling of the money stock might increase the price of luxury goods by 3 or 4 times since those who discover the new money early on feel richer. Relative prices shift as money enters the economy through the purchase of specific goods.

As prices rise, not only are relative prices distorted, but so also is the function of profit. Profits appear to be augmented by the price increases, but again, this is only due to "money illusion." Irving Fisher’s observation is of help to us:

“I remember particularly a long talk with one very intelligent German woman who kept a shop in the outskirts of Berlin. She gave all kinds of trivial reasons for the high prices. . . When I talked with her the inflation had gone on until the mark had depreciated by more than ninety-eight per cent, so that it was only a fiftieth of its original value (that is, the price level had risen about fifty fold), and yet she had not been aware of what had really happened. Fearing to be though a profiteer, she said: ‘That shirt I sold you will cost me just as much to replace as I am charging you.” Before I could ask her why, then, she sold it at so low a price, she continued: “But I have made a profit on that shirt because I bought it for less.

 She had made no profit; she had made a [economic] loss. She thought she had made a profit only because she was deceived by the ‘Money Illusion’. . She had kept her accounts in what was in reality a fluctuating unit, the market. In terms of this changing unit her accounts did indeed show a profit; but if she had translated her accounts into dollars, they would have shown a large loss. . . ” (392)

I am an economist by training. I don’t think in terms of price levels in my day to day life. I notice that the prices of goods change from time to time. Some of the change may be due to an increase in the money stock. Some may be from changes in demand due to preferences or to supply shocks. A change in price tells us nothing about why a price has changed. Uneven adjustment of prices changes the nature of monetary exchange. Humans think in terms of observed nominal prices. Losses are easier to stomach when they are written on a balance sheet as a nominal gain, as Fisher’s story shows. Even if all agents came to know of the increase in the money stock beforehand, their preparations cannot prevent the realization of errors in prediction of prices of specific goods that are inevitable for the vast majority of agents. Agents with expectations of an increase in the money stock cannot necessarily prevent a temporary increase in AD. Distortion of the profit and loss mechanism promotes this outcome.

Now that we've worked through this thought experiment, we are ready to consider what happens by considering a graph of aggregate demand, short-run aggregate supply, and long-run aggregate supply. We consider an increase in aggregate demand.

Two effects are working here. The short run effect, which temporarily elevates y, and the long-run effect, which dominates the short-run effect having P absorb the total change in the money stock. It is important that we do not interpret long-run and short-run as representing specific time span. These are categories that describe types of change. The long-run is the state to which the model eventually converges. Long-run changes always swamp short-run changes. It is possible that long-run effects set in very quickly so that short-run changes are hardly observed. Or short-run changes may last for an exceptionally long period of time. There is no measurement of time that can consistently define the long-run and short-run. 

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