In perfect competition, firms are considered to be price takers and there is ass
ID: 1178626 • Letter: I
Question
In perfect competition, firms are considered to be price takers and there is assumed to be tree entry and exit in the market. Suppose that firms can produce BS* at a cost of cn(q) = q2 + (n - l). where is the number of tons of BS produced and n is a firm index, n = 1.2.3,... Note that the firm index is a measure of efficiency in "setting up" a firm to produce BS. We assume that a firm can also decide not to produce BS, which entails a total cost of zero. Note that ' an integer, i.e. we only have "whole firms" possible. Also note that efficiency ensuies that if firm k is in the market, so is firm k -1, . Market demand for BS is given by the aggregate demand function q(P) = 10-P. where P is the price per ton of BS. Assuming perfect competition, characterize the long-run equilibrium for blubber strips. In particular, calculate the following and explain your answers. The aggregate supply function for an arbitrary number of firms in the market J. The equilibrium price ol BS and the long-run equilibrium number of linns J *. ticalling that the number ot firms must be an integer. Explain carefully.Explanation / Answer
Analogously, the concept of aggregate supply does not refer to a fixed number, but rather to a schedule (a supply curve). The volume of goods and services that profit-seeking enterprises will provide depends on the prices they obtain for their outputs, on wages and other production costs, on the state of technology, and on other things. The relationship between the price level and the quantity of real GDP supplied, holding all other determinants of quantity supplied constant, is called the economy's aggregate supply curve.
A typical aggregate supply curve is drawn in Figure 27-1. It slopes upward, meaning that as prices rise more output is produced, other things held constant. It is not difficult to understand why. Producers in the U.S. economy are motivated mainly by profit. The profit made by producing a unit of output is simply the difference between the price at which it is sold and the unit cost of production:
Profit per unit = Price - Cost per unit
So, the response of output to a rising price level--which is what the slope of the aggregate supply curve shows--depends on the response of costs.
Many of the prices that firms pay for labor and other inputs are relatively fixed for periods of time--though certainly not forever. Often, workers and firms enter into long-term labor contracts that set money wages up to 3 years in advance. Even where there are no explicit contracts, wage rates typically adjust only once a year. During the interim period, money wages are fixed. Similarly, a variety of material inputs are delivered to firms under long-term contracts at prearranged prices.
Why is it significant that firms often purchase inputs at prices that stay fixed for considerable periods of time? Because firms decide how much to produce by comparing their selling prices with their costs of production; and production costs depend, among other things, on input prices. If the selling prices of the firm's products rise while its wages and other factor costs are fixed, production becomes more profitable, and firms will presumably increase output.
A simple example will illustrate the idea. Suppose a firm uses I hour of labor to manufacture a gadget that sells for $9. If workers earn $8 per hour, and the firm has no other production costs, its profit per unit is:
Profit per unit = Price - Cost per unit
= $9 - $8 = $1
Now what happens if the price of a gadget rises to $10, but wage rates remain constant? The firm's profit per unit becomes:
Profit per unit = Price - Cost per unit
= $10 - $8 = $2
With production more profitable, the firm will likely supply more gadgets.
The same process operates in reverse. If selling prices fall while input costs are relatively fixed, profit margins will be squeezed and production cut back. This behavior is summarized by the upward slope of the aggregate supply curve: Production rises when the price level (henceforth, P) rises, and falls when P falls. In other words:
The aggregate supply curve slopes upward because firms normally can purchase labor and other inputs at prices which are fixed for some period of time. Thus, higher selling prices for output make production more attractive.1
The phrase "for some period of time" alerts us to an important fact: The aggregate supply curve may not stand still for long. If wages or prices of other inputs change, as they surely will during inflationary times, then the aggregate supply curve will shift.
SHIFTS OF THE AGGREGATE SUPPLY CURVE
We have concluded so far that, for given levels of wages and other input prices, there will be an upward-sloping aggregate supply curve relating the price level to aggregate quantity supplied. Now let us consider what happens when these input prices change.
THE MONEY WAGE RATE
The most obvious determinant of the position of the aggregate supply curve is the money wage rate. Wages are the major element of cost in the economy, accounting for more than 70 percent of all inputs. Since higher wage rates mean higher costs, they spell lower profits at any given prices. That is why companies like American Airlines and Caterpillar have staged fierce battles with their unions in recent years in an effort to reduce wages.
Returning to our example, consider what would happen to a gadget producer if the money wage rose to $8.75 per hour while the price of a gadget remained $9. Profit per unit would decline from:
$9 - $8 = $1
to
$9.00 - $8.75 = $0.25
With profits squeezed, the firm would probably cut back on production.
This is the way firms in our economy typically react to a rise in wages. Therefore, a wage increase leads to a decrease in aggregate quantity supplied at current prices. Graphically, the aggregate supply curve shifts to the left (or inward), as shown in Figure 27-2. In this diagram, firms are willing to supply $6,000 billion in goods and services at a price level of 100 when wages are low (point A). But after wages increase these same firms are willing to supply only $5,500 billion at this price level (point B). By similar reasoning, the aggregate supply curve will shift to the right (or outward) if wages fall. Thus:
A rise in the money wage rate makes the aggregate supply curve shift inward, meaning that the quantity supplied at any price level declines. A fall in the money wage rate makes the aggregate supply curve shift outward, meaning that the quantity supplied at any price level increases.
PRICES OF OTHER INPUTS
In this regard, there is nothing special about wages. An increase in the price of any input that firms buy will shift the aggregate supply curve in the same way; that is:
The aggregate supply curve is shifted inward by an increase in the price of any input to the production process, and it is shifted outward by any decrease.
While there are many inputs other than labor, the one that has attracted the most attention in recent decades is energy. Increases in the price of energy, such as those that took place in the early 1980s and again during the 1990 Gulf war, push the aggregate supply curve inward more or less as shown in Figure 27-2. By the same token, a rise in the price of any input we import from abroad would have the effect shown in the figure.
TECHNOLOGY AND PRODUCTIVITY
Another factor that determines the position of the aggregate supply curve is the state of technology. Suppose, for example, that a technological breakthrough increases the productivity of labor, that is, output per hour of work. If wages do not change, such an improvement in productivity will decrease business costs, improve profitability, and encourage more production.
Once again, our gadget company will help us understand how this works. Suppose the price of a gadget stays at $9 and the hourly wage rate stays at $8, but gadget workers become much more productive. Specifically, suppose the labor input required to manufacture a gadget falls from 1 hour (which costs $8) to three-quarters of an hour (which costs $6). Then profit per unit rises from
$9 - $8 = $1
to
$9 - $6 = $3
The lure of higher profits should induce gadget manufacturers to increase production--which is, of course, why manufacturers are constantly striving to raise productivity. In brief, we have concluded that:
Improvements in productivity shift the aggregate supply curve outward.
Figure 27-2 can therefore be viewed as applying to a decline in productivity. Since the 1970s, slow growth of productivity has been a persistent problem for the U.S. economy, one that we will examine in depth in Chapter 37.
AVAILABLE SUPPLIES OF LABOR AND CAPITAL
The last determinant of the position of the aggregate supply curve is obvious. The bigger the economy--as measured by its available supplies of labor and capital--the more it is capable of producing. So:
As the labor force grows or improves in quality, and as the capital stock is increased by investment, the aggregate supply curve shifts outward to the right, meaning that more output can be produced at any given price level.
This last aspect of the aggregate supply curve is central to the political debate over alternative supply-side strategies. Although neither party excludes the other factor of production, Republicans tend to concentrate on augmenting the supply of capital while Democrats tend to emphasize improvements in labor quality.
These, then, are the major "other things" that we hold constant when drawing up an aggregate supply curve: wage rates, prices of other inputs (such as energy), technology, labor force, and capital stock. While a change in the price level moves the economy along a given supply curve, a change in any of the other determinants of aggregate quantity supplied shifts the entire supply schedule.
EQUILIBRIUM OF AGGREGATE DEMAND AND SUPPLY
Chapter 25 taught us that the price level is a crucial determinant of whether equilibrium GDP is below full employment (a "recessionary gap"), precisely at full employment, or above full employment (an "inflationary gap"). We are now in a position to analyze which type of gap, if any, will actually occur in any particular case. By combining the analysis of aggregate supply just completed with the analysis of aggregate demand from the last two chapters, we can determine simultaneously the equilibrium level of real GDP (Y) and the equilibrium price level (P).
Figure 27-3 displays the mechanics. Aggregate demand curve DD and aggregate supply curve SS intersect at point E, where real GDP is $6,000 billion and the price level is 100. As can be seen in the graph, at any higher price level, such as 120, aggregate quantity supplied would exceed aggregate quantity demanded. There would be a glut on the market as firms found themselves unable to sell all their output. As inventories piled up, firms would compete more vigorously for the available customers, thereby forcing prices down. Both the price level and production would fall.
At any price level lower than 100, such as 80, quantity demanded would exceed quantity supplied. There would be a shortage of goods on the market. With inventories disappearing and customers knocking on their doors, firms would be encouraged to raise prices. The price level would rise, and so would output. Only when the price level is 100 are the quantities of real GDP demanded and supplied equal. Therefore, only the combination of P = 100, Y = $6,000 is an equilibrium.
Table 27-1 illustrates the same conclusion in another way, using a tabular analysis similar to that of Chapter 25 (refer back to Table 25-2, page 597). Columns 1 and 2 constitute an aggregate demand schedule corresponding to the aggregate demand curve DD in Figure 27-3. Columns 1 and 3 constitute an aggregate sup. ply schedule corresponding exactly to aggregate supply curve SS in the figure.
It is clear from the table that equilibrium occurs only at P = 100 and Y = $6,000. At any other price level, aggregate quantities supplied and demanded would be unequal, with consequent upward or downward pressure on prices. For example, at a price level of 90, customers demand $6,200 billion worth of goods and services, but firms wish to provide only $5,800 billion. The price level is too low and will be forced upward. Conversely, at a price level of, say, 110, quantity supplied ($6,200 billion) exceeds quantity demanded ($5,800 billion), implying that the price level must fall.