# Micro Lecture 10: Supply and Profit Maximization

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2 2 Market Supply Curve How many cans of beer would firms produce (the uantity supplied), if the price of beer were, given that everything else relevant to beer production remains the same. As figure 10.2 illustrates the market supply curve is the horizontal sum of each individual firm s supply curve. P If P=2.00 If P=1.50 If P=1.00 Firm A Firm B Market P P S A S B S If P=.50 Figure 10.2 Constructing the market supply curve Q Second Question: Where does an individual firm s supply curve come from; that is, how does a firm decide how much output to produce? Profit: The Firm s Goal Question: What is a firm interested in? Answer: Profit. What does profit eual? Profit = Total Revenues Total Costs = TR TC The firm will produce that uantity of output that makes its profit as large as possible; that is, the firm will produce its profit maximizing uantity of output. Your New Job: Consultant Mr. Busch, the president of Anheuser-Busch, hires you as a consultant. He wants to know if he is producing the profit maximizing uantity of beer; that is, Is Anheuser-Busch presently maximizing profit? If not, should more beer be produced or should less beer be produced? Question: What information would we need to determine whether or not a firm was maximizing its profits? That is, what information would we need to determine whether or not a firm is producing its profit maximizing uantity of output? Claim: We need to know the firm s marginal revenue and marginal cost: Marginal Revenue (MR) = Change in the firm s total revenue resulting from a one unit change in output. Marginal Cost () = Change in the firm s total cost resulting from a one unit change in output. More specifically, a firm is maximizing its profits only if marginal revenue euals marginal cost.

3 3 To convince you of this, first we will show that whenever marginal revenue exceeds marginal cost, the firm can increase its profits by producing more; to do so, suppose that MR = \$1.00 and =\$.80 If one more unit of If one more unit of output were produced output were produced TR would rise by \$1.00 TC would rise by \$.80 What would happen to profit if one more unit of output were produced? Profit = TR TC Since total revenue rises by \$1.00 and total costs rises by only \$.80, profits would increase by \$.20. In general, whenever marginal revenue is greater than marginal cost, profit can be increased by producing more output. Next, we want to show that whenever that marginal revenue is less than marginal cost a firm can increase its profit by producing less; to do this, suppose that MR = \$1.00 and =\$1.10 If one less unit of If one less unit of output were produced output were produced TR would fall by \$1.00 TC would fall by \$1.10 What would happen to profit if one more unit of output were produced? Profit = TR TC Since total revenue falls by \$1.00 and total costs falls by \$1.10, profits would increase by \$.10. In general, whenever marginal revenue is less than marginal cost, profit can be increased by producing less output. Generalizing: If marginal revenue exceeds marginal cost, a firm can increase its profit by producing more output. is less than marginal cost, a firm can increase its profit by producing less output. Therefore, whenever profits are being maximized, marginal revenue must eual marginal cost: MR > MR = MR < More production Profit Less production increases profit maximized increases profit Now what should we do? We will look at marginal revenue and marginal cost more carefully.

4 4 Marginal Revenue Curve This week we will study perfectly competitive industries, industries that are composed of a large number of small independent firms. In a perfectly competitive industry, no single firm's production decision can affect the price significantly; conseuently, each firm takes the price as a given, as a constant: Perfectly competitive industry Large number of small independent firms No single firm s production decisions can affect the price significantly. Each firm takes the price as a given, as a constant The American wheat industry provides a good example of a perfectly competitive industry. There are thousands of wheat farmers in the U.S. each of whom produces only a tiny fraction of total wheat production. That is, the wheat industry is composed of a large number of small independent firms. If one wheat farmer in Kansas decides to grow another bushel of wheat, will he/she have a significant effect on the price of wheat? Of course not. Claim: In a perfectly competitive industry, each firm s marginal revenue just euals the price of output. To justify this claim, let us review the definition of marginal revenue: Marginal Revenue (MR) = Change in the firm s total revenue resulting from a one unit change in output. What does a firm s total revenue eual? Suppose that the firm produces units today: Total Revenue Today = Price Quantity = P = P Constant in a perfectly competitive industry What happens when a firm in a perfectly competitive industry produces one more unit tomorrow, when increases from to + 1? Total Revenue Tomorrow = Price Quantity = P + 1 = P + P Constant in a perfectly competitive industry Note that the price is taken as a constant in a perfectly competitive industry. Since the uantity of output increases by 1 and the price remains constant, the firm s total revenues will rise by an amount just eual to the price. Therefore, marginal revenue euals the price in a perfectly competitive industry: Marginal Revenue = Price

5 5 As shown in figure 10.3, the marginal revenue curve of a perfectly competitive firm is horizontal, just eual to the price. MR Firm s Marginal Revenue Curve Price MR = Price Figure 10.3: Marginal revenue curve under perfect competition Marginal Cost Curve We will argue shortly that the marginal cost exhibits a phenomenon call increasing marginal cost. To do so, however, we will first discuss a less subtle phenomenon, increasing total cost. In this way, we will appreciate more fully exactly what increasing marginal cost is all about. Increasing Total Cost: As a firm produces more output, its total cost increases. It is easy to justify the notion of increasing total cost. To produce more output, a firm must use more labor, materials, etc.; conseuently, as a firm produces more output, its total costs must increase. This is not a very sophisticated idea. It is very straightforward. Increasing Marginal Cost: As a firm produces more output, its marginal cost (that is, the change in its total cost resulting from a one unit change in production) increases. This is a much more subtle notion. The notion of increasing marginal cost reflects the same phenomenon as the notion of decreasing marginal product. Marginal Product of Labor: Change in the uantity of output produced resulting from a one unit change in the amount of labor hired. Decreasing Marginal Product: As a firm hires more labor, the marginal product of labor (that is, the change in production resulting from a one unit change in labor) decreases. We will use an example to explain the notions of increasing marginal cost and decreasing marginal product to show that they are euivalent. That is, we will argue that they are two different ways of viewing the same phenomenon.

6 6 Example of Increasing Marginal Cost: Atkins' Apple Orchard This homespun example illustrates why a firm s marginal cost increases as the firm produces more output. Atkins Apple Orchard is located in South Amherst. Mr. Atkins, the owner of the orchard, hires a worker to pick the apples. Apple picker is paid \$10.00 per hour. The first column of table 10.1 represents the uantity of labor hired by Mr. Atkins; the second column the total number of apples picked; and the third column marginal product of labor. What is marginal product of labor? Marginal Product of Change in the uantity of output produced resulting from a = Labor one unit change in the amount of labor hired Labor Hired Total Apples Picked Marginal (hours) (bushels) Product of Labor Table 10.1 Let us now explain why the numbers in the table are sensible. Obviously, the first row makes sense. If Mr. Atkins hires no labor, no apples will be picked. If a worker is hired for one hour, he/she will walk from tree to tree, picking apples within arm s reach. The table reports that in one hour, a worker can pick 1 bushel of apples in this way. When we move from 0 hours of labor hired to 1 hour of labor hired, total apple production rises from 0.0 to 1.0 bushel; conseuently, the marginal product of the first hour of labor is 1.0 bushel. Now, what if the worker is hired for a second hour? He/she will continue to pick apples within arm s reach and will be able to pick a total of 2 bushels of apples in the 2 hours. When we move from 1 hour of labor hired to 2 hours, total apple production rises from 1.0 to 2.0 bushels; conseuently, the marginal product of the second hour of labor is still 1.0 bushel. What happens if the worker is hired for a third hour? More of the same. The worker continues to pick apples within arm s reach and will pick a total of 3 bushels in the 3 hours. When we move from 2 hours of labor hired to 3 hours, total apple production rises from 2.0 to 3.0 bushels; conseuently, the marginal product of the third hour of labor is still 1.0 bushel. The situation changes if the worker is hired for the fourth hour, however. The worker runs out of apples within arm s reach. Picking apples now becomes a more time-intense operation. The worker must use a ladder and move the ladder from tree to tree. Accordingly, total apple production only rises from 3.0 to 3.6 bushels of apples when four hours of labor are employed; conseuently, the marginal product of the fourth hour of labor decreases to 0.6 bushels. If the worker is hired for a fifth hour, marginal product diminishes again because the worker must now go after apples that are less accessible so it takes him/her longer to pick them. When we move from 4 hours of labor hired to 5 hours, total apple production rises from 3.6 to 4.0 bushels; conseuently, the marginal product of the fifth hour of labor decreases to 0.4 bushels.

7 7 Summary: What happens to marginal product as more labor is hired? Eventually, marginal product of labor decreases. This is known as diminishing marginal product: as more labor is hired the additional output resulting from an additional unit of labor diminishes. This is a general phenomenon experienced by all firms. It is easy to understand why this phenomenon occurs in the context of our apple orchard example. The reason is clear: diminishing marginal returns set in after the apple picker works 3 hours when he/she runs out of apples within arm s reach. When this occurs picking apples becomes much more time-intensive because the worker must go after apples that are less accessible. Conseuently, as more labor is hired, marginal product of labor diminishes. Now, we will use the table 10.1 to calculate Mr. Atkins cost of producing apples reported in table 10.2: Apples Picked Labor Hired Total Labor (bushels) (hours) Cost 0 0 \$ Table 10.2 To justify the total labor cost column in table 10.2, keep in mind that the apple picker is paid \$10 per hour. If he decides to produce no apples, Mr. Atkins would hire no labor; conseuently, his labor costs would be 0. 1 bushel of apples, he must hire 1 hour of labor; his total labor costs would be \$10. 2 bushels of apples, he must hire 2 hours of labor; his total labor costs would be \$20. 3 bushels of apples, he must hire 3 hours of labor; his total labor costs would be \$30. 4 bushels of apples, he must hire 5 hours of labor; his total labor costs would be \$50. Next, calculate his marginal cost. Recall the definition of marginal cost: Marginal Cost () = Change in the firm s total cost resulting from a one unit change in output. The change in Mr. Atkins total costs is the marginal cost as reported in the last column of table 10.3: Apples Picked Labor Hired Total Labor Marginal (bushels) (hours) Costs Cost 0 0 \$ Table 10.3 Marginal costs increase when diminishing marginal product sets in; that is, marginal cost increases after the apple picker works for 3 hours when he/she runs out of apples within arm s reach. Note that increasing marginal cost and diminishing marginal product are two sides of the same coin.

8 8 As a conseuence of diminishing marginal product, the firm s marginal cost increases as the firm produces more output; that is, the marginal cost curve is upward sloping as shown in figure A Firm's Production Decisions How many cans of beer would the firm produce? Figure 10.4: Marginal cost curve We can now answer this uestion. Recall that marginal revenue and marginal cost determines the firm s profit maximizing uantity of output: MR > MR = MR < More production Profit Less production increases profit maximized increases profit Also, recall what we have just learned about the marginal revenue and marginal cost curves: Marginal Revenue (MR) Curve Marginal Cost () Curve Horizontal Upward sloping MR = Price * is the firm s profit maximizing uantity of output because marginal revenue euals marginal cost when the firm is producing * units as shown in figure If the firm were to produce less than * units, the firm would not be content because marginal revenue would exceed marginal cost; when marginal revenue is greater than marginal cost, the firm could increase it profit by producing more. Similarly, if the firm were to produce more than *, it would not be content because marginal revenue would fall short of marginal cost; when marginal revenue is less than marginal cost, the firm could increase it profit by producing less. MR, Price MR = Price * MR > MR < Figure 10.5: Profit maximization

9 Micro Lecture 11: Supply, the Short Run, and the Long Run Review: Market Supply Curve Two Questions First Question: Where does the market supply curve come from? We will show that the market supply curve is the horizontal sum of each firm s individual supply curve. Second Question: Where does an individual firm s supply curve come from? That is, how does a firm decide how much output to produce? First Question: Where Does the Market Supply Curve Come From? Individual Firm s Supply Curve: Firm A P How many cans of beer would Firm A produce (Firm A s If P=2.00 uantity supplied), if the price of beer If P=1.50 were, given that everything else relevant to beer production If P=1.00 remains the same. Figure 11.1 illustrates the individual If P=.50 supply curve for Firm A. Figure 11.1: Firm A supply curve S A Market Supply Curve How many cans of beer would firms produce (the uantity supplied), if the price of beer were, given that everything else relevant to beer production remains the same. As figure 11.2 illustrates the market supply curve is the horizontal sum of each individual firm s supply curve. P If P=2.00 If P=1.50 If P=1.00 If P=.50 Firm A P Firm B P Market S A S B Figure 11.2 Constructing the market supply curve S Q

10 2 Second Question: Where does an individual firm s supply curve come from; that is, how does a firm decide how much output to produce? Firm s Goal: Maximize Profit Profit = Total Revenues Total Costs = TR TC Marginal Revenue and Marginal Cost Marginal Revenue (MR) Marginal Cost () Change in the firm s total Change in the firm s total revenue resulting from a one cost resulting from a one unit change in output. unit change in output. The relationship between marginal revenue and marginal cost tells us whether or not profit is maximized: MR > MR = MR < More production Profit Less production increases profit maximized increases profit Marginal Revenue and Marginal Cost Curves Figure 11.3 superimposes the marginal revenue and marginal cost curves to illustrate the profit maximizing uantity: 2.00 Marginal Revenue (MR) Curve Horizontal MR = Price Marginal Cost () Curve Upward sloping 1.50 If P = * MR> MR< MR = 1.00 Figure 11.3: Profit maximization when the price euals \$1.00

11 3 Therefore, we have just found one point on the individual firm s supply curve, the point corresponding to a price of \$1.00 per can. The blue point in figure 11.5 on the firm s marginal cost curve indicates how much beer the firm would produce if the price of beer were \$1.00 per can. Accordingly, the blue point is on the individual firms supply curve If P = Profit maximizing uantity of output if P=1.00 MR = 1.00 Figure 11.4: Firm A s production when the price euals \$1.00 How do we find another point on the individual firm s supply curve? Just choose another price. What if the price of beer were \$1.50 per can? Then marginal revenue would eual 1.50: MR = 1.50 The firm s profit maximizing uantity of output is where its marginal revenue euals its marginal cost. The second blue point indicates the uantity of output the firm would produce if the price were \$1.50 per can; conseuently, the second blue point in figure 11.6 is on the individual firm s supply curve also. Now, what do we observe? We have found two points that are on the individual firm s supply curve: the point representing the uantity supplied if the price were \$1.00 per can and the point representing the uantity supplied if the price were \$1.50 per can. These two points that lie on the supply curve also lie on the firm s marginal cost curve. It looks like the individual firm s supply curve is just its marginal cost curve. How can we be sure this is correct? Let us choose another price. What if the price were \$.50 per can? Then marginal revenue would eual.50: MR =.50 The firm s profit maximizing uantity of output is where its marginal revenue euals its marginal cost. The third blue point indicates the uantity of output the firm would produce if the price were \$.50 per can; conseuently, the third blue point in figure 11.7 is on the individual firm s supply curve also. Like the other two blue points, it lies on the firm s marginal cost curve also. If P = 1.00 Profit maximizing uantity of output if P=1.00 if P= Figure 11.5: Firm A s production when the price euals \$1.50 Figure 11.6: Firm A s production when the price euals \$.50 So, we have just shown that an individual firm s supply curve is its marginal cost curve. In reality, we must add one caveat to this statement. If the price becomes too low, a firm would have an incentive to go out of business rather than to continue to operate. We will address this in the next lecture..50 If P = 1.50 MR = 1.50 If P = 1.00 Profit maximizing uantity of output if P=.50 if P= if P=1.00 MR = 1.00 If P = 1.50 MR = 1.50 MR = 1.00 If P =.50 MR =.50

12 4 Short Run and Long Run: Going Out of Business To understand the behavior of firms, economists make a distinct between two time periods, the short run and the long run: Short Run: In the short run, a firm s actions are restricted by commitments which the firm made previously. For example, in the past, a firm may have entered into labor agreements, signed legal contracts, signed leases, etc. Long Run: However, commitments do not last forever. Labor agreements, contracts, and leases specify termination dates. The long run refers to the period of time after commitment expires. Preview: Going out of business in the short and long run: Short Run Long Run Price (P) and Price (P) and Average Variable Cost (AVC) Average Total Cost (ATC) P < AVC P < ATC Firm goes out of Firm goes out of business in the short run. business in the long run. Firm shuts down. Firm exits. Jeff Lord s Consulting Firm Until January 1, 2015, Jeff Lord, a business consultant, worked for Arthur Anderson earning a salary of \$25,000 a month. Anderson Salary: \$25,000 per month On January 1, 2015, he resigned from Arthur Anderson to start his own consulting firm. On that date: He signed a one-year lease for office space. The one-year lease legally reuires Jeff to pay his landlord \$20,000 per month in rent until January 1, He hired several employees whose wages summed to \$35,000 a month. All other out-of-pocket costs that Jeff incurs are negligible. Jeff departed from Anderson on very good terms; the management at Anderson told him that he could return to their firm anytime at his old \$25,000 per month salary. Immediately after Jeff began his business he acuired several loyal clients. Jeff charges his clients \$650 per hour and records 100 billable hours per month. In total, Jeff collects \$65,000 from his clients each month. It is now easy to calculate his monthly income: Price = \$650/hour Quantity: 100 hours Rent: \$20,000 per month Total Revenues = P Employee Wages: \$35,000 per month = = \$65,000 per month Jeff s income when operating = \$65,000 ( \$20,000 + \$35,000 ) his firm = \$65,000 \$55,000 = \$10,000

13 5 Accounting Costs, Opportunity Costs, and (the Economist s) Total Costs We will now use Jeff s consulting firm to generalize our notions of costs. Figure 11.7 illustrates accounting costs, costs from the perspective of the accountant: Accounting Costs: Jeff s accounting costs are \$55,000 per month. Accounting costs eual the payments the owner of the firm makes to others, the owner s out-of-pocket costs. In Jeff s case, accounting costs euals the rent Jeff pays his landlord and the wages he pays his employees: Accounting Costs = \$20,000 + \$35,000 = \$55,000 Accounting Costs \$55,000 Rent Employee Wages 20,000 35,000 Figure 11.7: Jeff s Accounting Costs We can now express the income Jeff earns when operating his firm more generally: Jeff s income when operating = \$65,000 ( \$20,000 + \$35,000 ) his firm = \$65,000 \$55,000 = \$10,000 = Total Accounting Revenue Costs In general, the income that an owner receives from his/her firm euals the firm s total revenue less its accounting costs. The economist s notion of costs is more inclusive than the accountant s. Economists include not only accounting costs but also opportunity costs. Recall the concept of opportunity cost: Opportunity Costs: Opportunity costs represent what the owner foregoes when he/she operates his firm. In Jeff s case, when he runs his firm, he must forego the salary he would have earned at Anderson. Jeff s Anderson salary is an opportunity cost: Opportunity Costs = \$25,000 Total Costs: Total costs eual the sum of accounting and opportunity costs: Total Costs = \$55,000 + \$25,000 = \$80,000 Total Costs (TC) \$80,000 Accounting Costs Opportunity Costs \$55,000 \$25,000 Rent Employee Wages Anderson Salary \$20,000 \$35,000 \$25,000 Figure 11.8: Jeff s Total Costs As seen in figure 11.8, total costs are the sum of accounting and opportunity costs.

15 7 Economists refer to all costs that are not fixed costs, all costs that are not bound by a fixed commitment, as variable costs as shown in figure 11.10: Variable Variable costs represent all costs that are not fixed in the short run: Costs: Variable Costs = Total Costs Fixed Costs = \$80,000 \$60,000 = \$20,000 Generalizing: Total Costs (TC) \$80,000 Accounting Costs Opportunity Costs \$55,000 \$25,000 Rent Employee Wages Anderson Salary \$20,000 \$35,000 \$25,000 Fixed Costs (FC) Variable Costs (VC) \$20,000 \$60,000 Figure 11.10: Jeff s Total Costs Jeff s monthly income if he continues to operate his firm = TR Accounting Costs Jeff s monthly income if he goes out of business in the short run = Opportunity Costs Fixed Costs Question: In fact, Jeff would not go out of business in the short run, but under what circumstances would the owner of a firm to so? Income the owner earns when operating his/her firm < Income the owner earns if he/she goes out of business in the short run Total Revenues Accounting Costs < Opportunity Costs Fixed Costs Moving Accounting Costs to the right hand side Total Revenues < Accounting Costs + Opportunity Costs Fixed Costs Total Costs = Accounting Costs Opportunity Costs Total Revenues < Total Costs Fixed Costs Variable Costs = Total Costs Fixed Costs Total Revenues < Variable Costs P < VC P < VC P < AVC Dividing by AVC = VC

16 8 Shutdown and the a Firm s Individual Supply Curve Shutdown Rule: A firm will go out of business in the short run, shutdown, whenever the price is less than its average variable cost. Terminology: We use the term shutdown to refer to a firm going out of business in the short run Individual Firm s Supply Curve Individual Firm s Supply Curve: The individual firm s supply curve is its marginal cost curve until the price is very low and falls below average variable cost. When the price is less than average variable cost, the firm will shut down in the short run and produce nothing. See figure Curve Shutdown: P<AVC Figure 11.11: Individual firm s supply curve

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