c 2007 Je rey A. Miron 6. The Meaning of Zero Pro ts: Fixed Factors and Economic Rent

Transcription

1 Lecture : Industr Sul. c Je re A. Miron Outline. Introduction. Short-Run Industr Sul. Industr Equilibrium in the Short Run. Industr Equilibrium in the Long Run. The Long-Run Sul Curve. The Meaning of Zero Pro ts: Fixed Factors and Economic Rent Introduction We have seen how to derive a rm s sul curve from its MC curve. A cometitive market will ticall have man rms, however, so industr sul consists of the sum of the sulies b the individual rms. We now derive the industr sul curve and the industr equilibrium in cometitive markets. Short-Run Industr Sul We start b considering the case of a xed number of rms, n. Let S i () be the sul curve of rm i; the industr or market sul curve is therefore

2 S() = nx S i () i= which is the sum of the individual sul curves. Geometricall, we are just using the sum of the quantities sulied b the rms in the industr at each rice, which gives the horizontal sum of sul curves:

3 Grah: Industr Sul Curve as Sum of Individual Sul Curves = x = x = :x 9 8 S() S() S() 8 9 Industr Equilibrium in the SR To nd the industr equilbrium, we use the industr sul curve in conjunction with the industr demand curve. Grahicall,

4 Grah: Industr Equilibrium = x = x 9 8 S() * D() 8 9 * This gives an equilibrium rice,, and an equilibrium quantit, q. We could also write down general or seci c equations for demand and sul, and solve these algebraicall for rice and quantit. These solutions, whether using grahs or algebra, do not tell us anthing of articular interest b themselves. But, we can use this framework to analze man imortant issues. To begin, it is useful to see the imlications of the equilibrium for the individual rms in the industr. We consider three ossibilities, deending on the cost curves of the articular rm. The rst ossibilit is one in which a given rm is making exactl zero ro ts; it is oerating at the oint on its MC curve that intersects the minimum of its AC curve:

5 Grah: A Cometitive Firm Earning Zero Pro ts MC AC AVC * = AC (*) * q For this rm, = c() This imlies that revenue equals costs, so this rm makes zero ro ts. A second ossibilit is that the rm is oerating at a oint on its MC curve above the minimum of the AC curve:

6 Grah: A Cometitive Firm Earning Positive Pro ts * > AC (*) Profits MC AC AVC * q For this rm, > c() This rm is making ro ts in the short-run equilibrium because revenue exceeds costs. Still a third ossibilit is that the rm oerates at a oint on the MC curve that is below the minimum of the AC curve:

7 Grah: A Cometitive Firm Earning Negative Pro ts MC AC AVC * < AC (*) * In this case < c() so revenue is less than costs, and the rm is making negative ro ts, i.e., a loss. It makes sense for this rm to sta in oeration if the rice is above average variable costs. This wa, it makes a smaller loss than shutting down entirel. Industr Equilibrium in the Long Run In the long run, each rm can adust its xed factors of roduction. from its short-run cost curves to its long-run cost curves. So, it can move However, if a rm is making losses in the long run, it has no reason to sta in the industr; it should exit instead.

8 So, the onl relevant art of a rm s sul curve in the long-run is the art on or above the AC curve; onl this art corresonds to non-negative ro ts. Similarl, if a rm is making ro ts, we exect entr to occur (assuming some rms have the aroriate cost curves). NB: If the cost of all factors is measured at market rice, everone should have the same access. The reason is that a rm that has a unique asset should be leasing this out at the market rice, not just hoarding it for itself. If no barriers to entr exist, the market is characterized b free entr. In man cases, barriers do exist: entr fees, ermits, legal barriers, regulations, licenses, etc. As rms enter or exit, this a ects the amount of stu roduced, and therefore equilibirum rice. What does the nal equilibrium look like? Assume now that all rms have an identical long-run cost function, c(): Given this cost function, we can comute the outut level where costs are minimized; call this : Let = c( ) be this minimum value of AC. This is the lowest rice that can be charged, and still have all rms breaking even (and therefore willing to sta in the industr). Now consider a grah that shows industr sul for di erent numbers of rms in the industr: 8

9 Grah: Industr Sul with Free Entr = x = x = x = x= = ' 9 8 * = min AC D() 8 9 The rst sul curve is for one rm; the second for two rms; and so on. The amount of outut sulied at an rice goes u linearl with the number of rms if all of them have the same sul curves. The equilibrium rice is the lowest one consistent with non-negative ro ts. In this diagram, it occurs for three rms; in this case, more than three is too man. It is useful to note that at this equilibrium oint, each rm is making ositive ro ts, as in the second case above. 9

10 The Long-Run Sul Curve So far, the method we have described for nding an equilibrium is to kee drawing industr sul curves for more and more rms until we nd the largest number of rms that is consistent with non-negative ro ts. Now consider a useful aroximation to that aroach. We want to construct one industr sul curve out of the n curves. We can rule out all the oints below : We can also eliminate oints that are too far out on an given sul curve, assuming downward-sloing demand:

11 Grah: Points Too Far Out a Given Sul Curve So, the relevant ortions are those in this grah:

12 Grah: The Long-Run Sul Curve * Note that the curve gets atter and atter. Wh? With more rms in the industr, a given increase in rice elicits a given outut resonse from more rms. With lots of rms, the sul curve gets ver at. So, a reasonable aroximation is that the long-run industr sul curve is at at a rice equal to the minimum of the AC curve.

13 Grah: The Long Run Sul Curve: Minimum AC 9 8 * * = min AC 8 9 This imlies that in the long-run equilibrium, rofts cannot be much above zero. If rms were earning substantial ro ts, entr would occur. NB: This is imlicitl assuming that each rm (or, the level of outut that minimizes AC) is small relative to overall market demand. Again, note that if all factors are being measured and riced roerl as oortunit costs, a rm earning ositive ro ts can be exactl dulicated. NB: It is imortant to kee in mind the correct de nition of costs and ro ts. All factors are getting their oortunit costs: owners of labor, caital, etc. So, rms do not earn ure economic roft. Firms can, however earn ro t in the accounting sense, and rm owners are getting (just) enough to make them want to sta in the business. The LR equilibrium of a cometitive industr with free entr looks like the longrun sul curve of a rm with constant returns to scale. In one case, a given rm is dulicating roduction at the same costs; in another case, di erent rms are doing the dulication.

14 Fixed Factors and Economic Rent It is also useful to consider the case without free entr, even in the long-run. some cases, the number of rms might be xed. In The main reason is that certain factors of roduction are in xed sul. A standard examle is resource extraction industries, such as oil. Other examles include agriculture (land), aseball teams, the movie industr, universities (talent), etc. Legal barriers exist as well: taxi medallions, the liquour industr, medical schools, rofessional licensure, etc. Given this, it might look like an industr can oerate with ositive ro ts in the long run. This is not correct. It is more likel that we are not aroriatel measuring the market value of whatever is reventing entr. We should value each inut at its market rice = oortunit cost. If it aears the farmer is making ositive ro t, e.g., it is because we have forgotten to subtract the cost of his land. Sa, after doing the math, farmer is earning. What would someone a to rent the land?. Then this erson could hire the farmer and have him do exactl what he had been doing. Note that what matters is not what the land originall cost; what matters is what it can sell for. Whenever a xed factor is reventing entr, a rental rate for that factor exists. Thus, the ossibilit of entr drives ro ts to zero. This otential entr means cometition for the xed factors, which raises their rices, which in turn makes ro ts zero.

15 The examles above are instances of economic rent: aments to a factor of roduction in excess of the minimum necessar to have that factor sulied. From the view oint of the econom as a whole, the rice of agricultural roducts determines the value of agricultural land. From the view oint of the farmer, the value of his land is a cost of roduction that enters the ricing of his roduct. See this grah:

16 Grah: Economic Rent for a Fixed Factor economic rent q In this case, AVC reresents the average cost for all factors excluding land. The aarent ro ts are the area of the box ; this equals economic rents, the amount land would rent for in a cometitive market. The average cost curve includes the oortunit cost of the land. correctl, economic ro ts to oerating the farm will be exactl zero. Measured That is, c v ( ) rent = or rent = c v ( ) We can see from this analsis that the equilibrium rice determines rent, not the reverse. The rm sulies along its M C curve, which is indeendent of exenditure on the xed factors. Rent is then adjusted to drive ro ts to zero.

17 What is the signi cance of rent versus ro ts? The land owner is not making a ro t in oortunit cost terms; the return to e ort at farming is the same as in other activities. Similarl, the stock market rate of return in industries with scare xed factors should be no higher than the return in other industries.