Aggregate Supply. MPL i = Y i / L i

Transcription

1 Aggregate Supply The upply of output depend on the behavior of producer. roducer' chooe the quantity of input to employ. Thee input produce output and we aume that producer chooe their input to maximize their profit. To tudy thi deciion, we focu on a ingle input, work effort. Our concluion would not change if we increaed the number of input. We compare the benefit of hiring an additional unit of work effort with the cot of hiring an additional unit of work effort. We begin with the benefit ide. the marginal product of labor The firm hire additional work effort in order to produce output. The firm ell the output to garner additional revenue. The change in total output brought about by a unit change in work effort i called the marginal product of labor (ML). We write the marginal product a ML i = i / L i We have placed a upercript over ML to indicate that we are examining the behavior of an individual producer. The marginal product of labor ha everal important propertie. Firt, given the level of other input, the ML diminihe a the quantity of work effort increae. The diminihing marginal product occur becaue each additional unit of work effort ha le of the given input with which to work. For example, uppoe you have 0 worker and 80 hour of computer time o that the average worker get 8 hour of computer time. Now if you add an additional worker, the new worker (and the average worker) only have 80/ = 7.27 hour of computer time. Since the new worker ha le computer time, the new worker will add le to output than her predeceor. Several factor can change the marginal product of labor. For example, if better oftware i placed on the computer, new worker will be more productive. If new computer are added, thi will raie the marginal product. For example, if the firm purchae another 20 hour of

2 2 computer time, the new worker will have 00/ = 9.09 hour of time, intead of 7.27 hour, and thi increae can be expected to raie her productivity. In general, an improvement in technology or increae in the capital tock will permanently increae labor' marginal product. There are ome factor that will temporarily change the ML. Bottleneck, dilocation, and labor trike can temporarily interrupt production and reduce labor' productivity. A temporary increae in the price of an important input, uch a energy, can alo impair labor' productivity. Other factor, uch a weather, may alo affect the ML. We can ummarize our dicuion of the determinant of the ML with the table Table : Shock to the ML ermanent Temporary technology + bottleneck, dilocation, trike - capital tock + temporary increae in the price of energy (or other important natural reource) - natural reource + good production weather + Thi lit i not exhautive. Other hock, uch a change in law or culture, may permanently alter productivity and other yet, uch a natural catatrophe, may temporarily affect the ML. the hiring deciion A producer who hire an additional unit of work effort receive an additional ML i unit of output. Each unit of output ell for the price i and o the firm receive the additional revenue i $ ML i from an additional unit of work effort. Thi additional revenue i called the marginal revenue product of labor. The additional cot of hiring another unit of labor i the wage, W. In principle, the wage i not jut the wage or alary paid to the worker, but alo include other cot uch a the employer contribution to ocial ecurity, unemployment compenation, and the value of fringe benefit. Conider the cae where i $ ML i > W

3 3 In thi cae, the benefit of adding an additional unit of work effort exceed the cot, o the firm hould continue hiring. On the other hand, if i $ ML i < W then the benefit of hiring an additional unit of work effort fall hort of the additional cot, and the firm hould reduce (or not hire in the firt place) it work effort. The producer will be happy with their level of work effort when i $ ML i = W. In hort, profit maximizing producer will hire an amount of work effort that make the marginal revenue product equal the wage. It turn out to be convenient to put thi relationhip in term of the relative price and real wage, o we divide both ide of thi equation by the price level,. Thi give u ( i /) $ ML i = W/ and reveal that the producer' deciion depend on her relative price, i /, the real wage, W/, and the marginal product of labor. hock to the hiring deciion Change in any of thee factor will change the hiring and production deciion. For example, uppoe the relative price of thi producer' output increae. Initially, thi make ( i /) $ ML i > W/ and the firm will increae it hiring and o alo the output it produce. We conclude that an increae in the relative price that a firm charge lead to an increae in the output of that producer. Now uppoe there i a temporary increae in the price of energy. Since worker have le of thi natural reource with which to work (and probably le capital a well ince it i more cotly to power machine), the marginal product of labor will fall. Initially thi make ( i /) $ ML i < W/ and firm will fire or layoff work effort. Thi adjutment implie that

4 4 output will fall in the face of a temporary change in the price of energy. In general, hock that reduce the marginal product of labor will caue output to decline, while hock that improve labor' marginal product will caue output to increae. Suppoe worker experience a hift in preference toward leiure. Worker will begin to exit the work force and thi reduction in labor upply will drive the real wage up. Thi increae in the real wage will initially caue ( i /) $ ML i < W/ and firm will hire fewer worker and output will decline until the equality i retored. Alternatively, uppoe an economy experience a large wave of immigration. The additional worker will increae the upply of work effort and drive real wage down. Thi reduction in the real wage will encourage firm to hire worker and raie real output. Finally, uppoe union are ucceful in raiing the real wage in important ector of the economy. Thi raie will lead firm to hire fewer worker and output will fall. the long run aggregate upply curve In the long run all price are flexible and all price information i known. That i to ay, all deciion are baed on correct information in the long run. Now uppoe in the long run all price, wage, and nominal variable double. What i the effect of thi price change on output? If all price and wage double, then there will be no change in the relative price of any firm or in the real wage. Since marginal product do not depend on price, o there will be no change in any ML. In thi cae, no one hiring deciion will be diturb and no firm will change it work effort or output deciion. LAS 2 * Figure : The Long Run Aggregate Supply Curve

5 5 A picture of thi reult i hown in Figure. At the initial price level, output of all producer i *. When all price double to 2, output tay at *. Thi reult implie that in the long run output doe not depend on the price level. The vertical LAS curve in Figure repreent thi independence. The vertical LAS doen't mean that the LAS can never move. For example, an improvement in technology or the accumulation of capital will caue the LAS curve to hift out and to the right. the hort run aggregate upply curve In the hort run, deciion are not baed on complete information. In particular, we take the hort run to be a period hort enough that producer do not know the overall price level,. Intead they form ome expectation or perception, e, about the price level. We want to know what happen to output when the price level unexpected increae, ay from to 2. Since the price level ha increaed, the typical producer ee their price i increae, but ince thi increae i unexpected, they believe the price level ha not changed, or not changed by much, and o believe their relative price, i /, ha rien. We know that when producer believe their relative AS 2 * 2 Figure 2: The Short Run Aggregate Supply Curve price ha increaed, they repond by increaing their output. Thi miperception occur acro the board o the typical or average firm increae their output and o aggregate output increae a well, from * to 2 in Figure 2.

6 6 Of coure, output will not tay at 2 permanently. Sooner or later, producer will learn that all price have rien o that the increae in their relative price wa but an illuion, and output will return to it long run level, *. LAS e AS 2( = ) 2 AS e ( = ) 2 * 2 Figure 3: The Long and Short of It We conider the relationhip between the long run and hort run aggregate upply curve in Figure 3. Suppoe we begin in a long run ituation. In the long run, people expectation are correct, o currently people expect the price level to be. Thi mean the hort curve, AS, i drawn on the aumption that e =. Now uppoe that the price level unexpectedly rie to 2. In the hort run, thi caue an increae in output to 2. Thi increae in price i interpreted by firm a an increae in their relative price, hiring increae, and total output increae to 2. Firm eventually learn that they were mitaken. Once they realize their relative price ha not increaed, they cut back on work effort and output return to *. In Figure 3 the realization of the firm that all price are higher caue a hift in the hort run aggregate upply curve back and to the left. When expectation have fully adjuted to the price level 2, o that e = 2, output return to *, and the hort run aggregate upply curve become AS 2. hock to hort run aggregate upply Jame Hamilton, an economit at the Univerity of California at San Diego, ha hown that all but one of the pot World War II receion wa immediately preceded by or concurrent

7 7 LAS AS 2 AS 2 * Figure 4: A Temporary Increae in the rice of Oil with a harp increae in the price of oil. Ever ince the OEC oil price hock of the 970 economit in general have acknowledged the role of upply hock in the economy. In our model a temporary increae in the price of oil lower the marginal product of labor. A we noted earlier, at any given price level thi decreae caue firm to reduce their work effort and output decline. Thi change implie that the AS curve hift back and to the left. Thi hift i depicted in Figure 4. Not all upply hock, even temporary one, are bad. Suppoe, for example, the weather take a turn for the better. Temperature and rain are jut perfect for agriculture and contruction. In thi cae, the marginal product of labor will increae, hiring will expand, and output will increae. Thi will caue the AS curve to hift out and to the right. ummary Work effort and output are determined by the profit maximizing deciion of firm and the willingne of houehold to upply work effort. If firm perceive an increae in their relative price, it become profitable to hire additional worker, and work effort and output will increae. An increae in the marginal product of labor will alo make it profitable to increae work effort and output. Change in labor upply that drive up real wage will make it unprofitable to maintain the ame work effort, o firm will reduce work effort and output will fall.