How To Calculate Profit Maximization In A Competitive Dairy Firm

Transcription

1 Microeconomic FRQ s Bestmilk, a typical profit-maximizing dairy firm, is operating in a constant-cost, perfectly competitive industry that is in long-run equilibrium. a. Draw correctly-labeled side by side graphs for the dairy market and for Bestmilk showing the following: price and output for the industry and price and output for Bestmilk. b. Assume that milk is a normal good and consumer income falls. Assume that Bestmilk continues to produce. On your graph in part a, show the effect of the decrease in income on each of the following in the short-run: price and output in the industry, price and output for Bestmilk, area of loss or profit for Bestmilk. c. Following the decrease in consumer income, what must be true for Bestmilk to continue to produce in the short-run? d. Assume that the industry adjusts to a new long-run equilibrium. Compare the following between the initial and the new long-run equilibrium: price in the industry, output of a typical firm, the number of firms in the dairy industry. Scoring guidelines and answers P S P P1 P1 MR1 P2 P2 MR2 D1 D2 MC ATC ATC intersects MR1 at ATC s minimum; line from q2 intersects ATC; shaded area represents loss following D decrease Q2 Q1 Q q2 q1 Q INDUSTRY BESTMILK a. 4 pts. 1 for graph of industry, 1 for industry P & Q, 1 for horizontal D for Bestmilk, 1 for equilibrium Q where P=MC=ATC. b. 4 pts. 1 for decrease in D, 1 for decrease in market (industry) P and Q, 1 for change to new lower profit-maximizing P and Q for Bestmilk, 1 for shading the area of loss for Bestmilk c. 1 for stating that P>AVC, or TR>TVC, or stating that losses are less than total fixed costs d. 3 pts. 1 for stating that price returns to original long-run equilibrium price, 1 for stating that output of a typical firm returns to original profit-maximizing quantity, 1 for stating that there is a decrease in the # of firms. Supply + tax P A 13 B Supply 12 C F D G Demand 11 E Q 2. The graph above shows the market for a good that is subject to a per-unit tax. The letters in the graph represent the enclosed areas. a. Using the labeling on the graph, identify each of the following: equilibrium price and quantity before the tax, area representing consumer surplus before the tax, area representing producer surplus before the tax. b. Assume that the tax is now imposed. Based on the graph, does the price paid by the buyers rise by the full amount of the tax? Explain. c. Using the labeling on the graph, identify each of the following after the imposition of the tax: net price received by the sellers, amount of tax revenue, area representing consumer surplus, area representing deadweight loss. Scoring guidelines and answers a. 3 pts. 1 pt. for P = $12 and Q = 100 units; 1 pt. for identifying consumer surplus before the tax (CS = A+B+C+F); 1 pt. for identifying producer surplus before the tax (PS = D+E+G = $100) b. 2 pts. 1 pt. for stating that the price paid by the buyers does not increase by the full amount of the tax; 1 pt. for correct explanation: P increases by $1 and the tax is $2 per unit. c. 4 pts. 1 pt. for identifying the net price received by the sellers, $11; 1 pt. for identifying the tax revenue, B+C+D or $160; 1 pt. for identifying consumer surplus, A; 1 pt. for identifying deadweight loss, F+G or $20.

2 3. P&L is a profit-maximizing shirt manufacturing firm. The firm can sell all the shirts it can produce to retailers at a price of $20 each. P&L can hire all the workers it wants at a market wage of $120 per day per worker. The table below shows the firm s short-run production function. # of workers # of shirts per day a. In what kind of market structure does this firm sell its output? How can you tell? b. In what kind of market structure does this firm hire its workers? How can you tell? c. Calculate the marginal revenue product of the 3 rd worker. Show your work. d. How many workers should the firm hire to maximize profit? Explain. Scoring guidelines and answers a. 2 pts. 1 pt. for identifying perfect competition; 1 pt. for correct explanation, price is constant or the firm is a price taker b. 2 pts. 1 pt. for identifying perfect competition; 1 pt. for correct explanation, price is constant or the firm is a price taker in the labor market c. 2 pts. 1 pt. for stating the MRP is $400; 1 pt. for showing the calculation: MRP = P x MP so MRP = $20 x 20 = $400 d. 2 pts. 1 pt. for indicating 6 workers, or in between 6 and 7 workers; 1 pt. for correct explanation: MRP > Wage for 6 th worker but MRP < Wage for 7 th worker (7 th worker adds 5 shirts so 5 x $20 (P of shirt) = $100; wage for 7 th worker is $120) The production of good X creates an externality. The following questions are based on the graph above, which show s the marginal revenue, marginal social benefit, marginal private cost, and marginal social cost associated with the production of good X. a. Is the externality positive or negative? Explain. b. Using labeling from the graph above, identify the socially optimum output. Explain how you determined your answer. c. Suppose that good X is produced by a profit-maximizing monopoly. Answer each of the following. i. Using labeling from the graph above, identify the unregulated firm s output. Explain how you determined your answer. ii. To produce the socially optimum output, indicate whether the government should tax or subsidize the firm. iii. Calculate the dollar value of the needed per-unit tax or subsidy.

3 d. Suppose that good X is produced in a perfectly competitive industry. Answer each of the following. i. Identify equilibrium output in the absence of regulation. Explain how you determined your answer. ii. To produce the socially optimum output, indicate whether the government should tax or subsidize the firms in the industry. iii. Calculate the dollar value of the needed per-unit tax or subsidy. 2. The graph above shows the demand for oil by US residents, the supply of oil by US producers, and the world price of oil. Use the labeling of the graph to answer the following questions. a. Identify the following before international trade occurs. i. Price of oil in the US market ii. Quantity of oil produced in the US market b. Now assume that the US begins to import oil at the world market price of Pw. Identify the quantity imported by the US. c. Identify the consumer surplus in the US market for each of the following cases. i. Before international trade ii. After international trade d. Identify the producer surplus in the US market for each of the following cases. i. Before international trade ii. After international trade 3. Assume that a profit-maximizing firm in a monopolistically competitive industry is in long-run equilibrium. a. Draw a correctly labeled graph that shows the profit-maximizing firm s price and output. b. Assume that the city in which this industry operates eliminates the business license fee (a fixed cost) for all firms in this industry. How does the elimination of the license fee affect each of the following for the individual firm in the short run? Explain your answers. i. Output ii. Economic profits Scoring guidelines and answers total pts. a. As shown on the graph, MSC>MPC indicates the existence of a negative externality. 2 pts.: 1 for identifying the negative externality; 1 MSC > MPC b. Socially optimal quantity = Q2 b/c MSB = MSC at this output level; 2 pts: 1 identifying Q2; 1 MSB = MSC c. Profit-maximizing quantity is Q1 b/c MR = MPC at this output level. To produce the socially optimum quantity, the government should grant the monopolist a per-unit subsidy of $3; 4 pts.: 1 identifying Q1; 1 at Q1, MPC = MR (or MC = MR); 1 subsidize firm; $3 per unit d. Equilibrium quantity for perfectly competitive industry is Q3 b/c MPC = D(MSB) at this output level. To produce the socially optimal quantity, the government should levy a per-unit tax of $5 on firms in this industry; 4 pts.: 1 identifying Q3; 1 MSB = MPC; 1 tax the industry; 1 -- $5 per unit 1. a. The externality is negative, because the social cost for each additional unity is higher than the private cost for that unit. b. The socially optimal output is at Q2, because that is where marginal social cost = marginal social benefit.

4 c. i.) An unregulated monopoly would produce at Q1, because that is where the marginal production cost (marginal private cost) = marginal revenue ii.) To move output from Q1 to Q2, a government subsidy is required. iii.) The subsidy should be #3 per unit. This would push marginal private costs down to $4, which would then intersect the marginal revenue curve at Q2, the desired output. d. i.) A perfectly competitive firm would produce at an equilibrium output of Q3, because that is where their marginal private cost = demand. ii.) To move output from Q3 to Q2, the government should tax the industry. iii.) A $5 tax is needed, which would move the marginal private cost curve up to $12. This makes the marginal private cost intersect the demand curve at the desired output of Q total pts. a. As shown on the graph, P2 and Q2 were the price and quantity of oil before trade in the US market; 2 pts.: 1 each identifying P2 and Q2 b. The amount of oil imported into the US market after trade would be equal to Q3 Q1. US production drops to Q1 but quantity demanded rises to Q3; 1 pt identifying (q3 Q1) or H-J c. The triangle P2KG represents consumer surplus before trade, while triangle PwKH represents consumer surplus after trade (1 pt. each) d. The triangle P1P2G represents producer surplus before trade, while triangle P1PwJ represents producer surplus after trade (1 pt. each) e. The triangle JGH shows the net gain in total surplus from trade (1 pt) 3. 8 pts. a. The correct graph for a monopolistically competitive firm will show a downward-sloping D curve with a downwardsloping MR curve below it. The firm s price and output would be found at the equality of MR and MC. In the longrun, the ATC curve is tangent to the demand curve and equal to price directly above the output level at which MR = MC. (see graph below); 4 pts.: 1 graph w/ downward-sloping D curve w/ correctly labeled axes; 1 downwardsloping MR curve below the D curve; 1 Q from MR = MC and P from D directly above Q; 1 long-run equilibrium AC (or ATC) tangent to D at Q b. When the fixed cost decreases, MC is not affected so that the output and price remain constant. Economic profit increases since ATC falls; 4 pts.: 1 individual firm s output does not change; 1 license fee is a fixed cost, thus it does not affect the firm s marginal cost; 1 economic profits increase; 1 explanation a. (graph) b. i.) output would not change; Output is determined by the point where marginal revenue equals marginal cost. If fixed costs change, the average total cost decreases but marginal cost does not change. ii.) Profits increase. The firm moves from earning normal or zero economic profit to earning an economic profit. The average total cost curve decreases below the demand curve. Demand remains the same and since output doesn t change, price stays the same. The cost though is now below price and the firm is making an economic profit Form B 1. Due to a new technology, Brunelle, Inc. enjoys monopoly power. Brunelle does not engage in price discrimination.

5 a. Explain why the demand curve lies above the marginal revenue curve. b. Assume that Brunelle is earning short-run economic profits. Using a correctly labeled graph, show the following for Brunelle. i. Profit-maximizing level of output, labeled as Q* ii. Profit-maximizing price, labeled as P* iii. Economic profits as a shaded area c. If Brunelle wants to maximize its total revenues instead of profits, using the graph from part b show the following. i. Revenue-maximizing level of output labeled as Qr ii. Revenue-maximizing price, labeled as Pr d. Given your answer in part b, indicate whether Brunelle is producing the allocatively efficient level of output. Explain. e. Explain what wil happen to Brunelle s demand curve as other firms adopt the same technology. 2. In each part below, assume that the government imposes a per-unit sales tax and that the supply curve is upward-sloping. a. In industry X, consumers buy the same quantity no matter what the price is. i. Using a correctly labeled graph, show what happens to the quantity sold when the tax is imposed. ii. How will the burden of the tax be distributed between buyers and sellers? b. In industry Y, the market demand curve is perfectly elastic. i. Using a correctly labeled graph, show what happens to the price of the good that he consumers pay when the tax is imposed. ii. How will the burden of the tax be distributed between buyers and sellers? c. In industry Z, the market demand curve is downward-sloping. Using a correctly labeled graph, shad the area that represents total tax revenues. 3. The diagram above shows the domestic supply and demand for good X in the country of Placonia. a. If the current world price of good X is Pw, does Placonia export or import good X? Explain. b. Given your answer in part a, indicate the quantity of good X that Placonia exports or imports. c. Assume that the government of Placonia imposes a tariff on good X, increasing the price from Pw to Pt. Using labels in the graph, indicate the change in each of the following in Placonia. i. Consumer surplus ii. Producer surplus d. Indicate how employment in the domestic industry that produces good X is affected by the tariff. Scoring guidelines and answers 1. 9 pts. a. 1 pt. Brunelle must lower its price on all units to sell additional units. Thus, the additional revenue from the last unit sold is the price minus the loss on units that would otherwise sell at a higher price.

6 b. 4 pts: 1 correctly labeled graph w/ downward-sloping D and MR below demand; 1 for Q* at MC=MR; 1 for P* at the height of the demand curve above MC=MR; 1 for shading the correct area of profit (P* - ATC)Q* c. 2 pts: 1 for identifying Qr at MR=0; 1 for identifying Pr at the height of the demand curve above Qr d. 1 pt. Brunelle is not producing the allocatively efficient level of output b/c P>MC (MSB > MSC) e. 1 pt. Brunelle s demand curve will shift inward to the left 1. a.) As Brunelle, Inc enjoys monopoly power, its demand curve is the demand curve for the industry and is therefore downsloping. Brunelle needs to lower the price of its product in order to sell more output, but this lower price also applies to all previous units of output produced, resulting in a marginal revenue curve that is lower than its demand curve. b.) (see graph) c.) As shown above, total revenue is maximized at the level of output which MR = 0 and the Pr is the price level of this quantity along the demand curve. d.) No it is not. At Q*, Brunelle is producing at a price that is above the marginal cost the firm faces (P>MC). In this scenario, there is an underallocation of resources, as society is willing to pay more for the good than it is for other uses of the money. e.) Shift inward to the left 2. 6 pts. a. 2 pts: 1 perfectly inelastic demand curve showing that Q does not change; 1 since producers can raise the price by the full amount of the tax, the tax falls entirely on buyers b. 2 pts.: 1 horizontal demand curve showing that price does not change; 1 the tax falls entirely on sellers since they can t charge more and thus must absorb the entire amount of the tax c. 2 pts.: 1 for shifting either the supply or the demand curve inward to the left; 1 for shading the correct profits area

7 2. a.: i.) the tax makes the supply curve shift to the left. But since the demand is perfectly inelastic, the quantity sold does not change. ii.) As seen in the graph, the burden falls entirely on consumers. b. i.) As the supply curve shifts to the left, the quantity sold decreases from Q1 to Q2 in the graph. ii.) As seen in the graph, the burden of tax falls entirely on suppliers of the good. c. The tax revenue is shown in the graph above. Goods are sold at P2 and Q2. The tax paid is (P2 P0) for each unit sold. The quantity sold is Q2. So the total tax revenue is (P2 P0) x Q pts: a. 2 pts: 1 Placonia imports the good; 1 the domestic opportunity cost of producing good X is higher than the world price (Pw) for unit JN. Or they can get it cheaper at the world price b. 1 pt. They import 300 (350 50) units or JN units c. 2 pts: 1 consumer surplus decreases from PwNH to PtMH, or a decrease of MNPwPt; producer surplus increases by JKPtPw d. 1 pt: Employment would increase b/c domestic production of good X increases in Placonia a.) Placonia imports good X because its domestic equilibrium price is higher than the world price, therefore it would be inclined to buy good X cheaper from abroad. b.) Placonia imports 300 units of good x (quantity demanded at point N (350) minus quantity supplied at point J (50)) c.) i. consumer surplus would change from area NHPw to area MHPt ( a net change of PtMNPw); ii producer surplus would change by area PtKJPw d.) Because of the tariff, more of good X will be produced domestically, therefore employment in the industry will increase. 1. J & P Company operates in a perfectly competitive market for smoke alarms. J & P is currently earning short-run positive economic profits. a. Using correctly labeled side-by-side graphs for the smoke alarm market and J &P Company, indicate each of the following for both the market and the J & P Company. i. Price ii. Output b. In the graph in part for J & P, indicate the area of economic profits that J & P Company is earning in the short run. c. Using a new set of correctly labeled side-by-side graphs for the smoke alarm market and J & P Company, show what will happen in the long run to each of the following. i. Long-run equilibrium price and quantity in the market ii. Long-run equilibrium price and quantity for J & P Company d. Assume that purchases of smoke alarms create positive externalities. Draw a correctly labeled graph of the smoke alarm market. i. Label the market equilibrium quantity as Qm ii. Label the socially optimum equilibrium quantity as Qs e. identify one government policy that could be implemented to encourage the industry to produce the socially optimum level of smoke alarms. 2. a. Draw a correctly labeled graph showing a typical monopoly that is maximizing profit and indicate each of the following. i. Price ii. Quantity of output iii. Profit

8 b. describe and explain the relationship between the monopolist s demand curve and marginal revenue curve. c. Label each of the following on your graph in part a i. Consumer surplus ii. Deadweight loss 3. Assume that Company XYZ is a profit-maximizing firm that hires its labor in a perfectly competitive labor market and sells its product in a perfectly competitive output market. a. Define the marginal revenue product of labor (MRPl). b. Using correctly labeled side-by-side graphs, show each of the following. i. The equilibrium wage in the labor market ii. The labor supply curve the firm faces iii. The number of workers the firm will hire c. Company XYZ develops a new technology that increases its labor productivity. Currently this technology is not available to any other firm. For Company XYZ, explain how the increased productivity will affect each of the following. Scoring guidelines and answers i. Wage rates ii. Number of workers hired pts: a. 4 pts.: 1 market graph w/ downward-sloping D curve and an upward-sloping S curve; 1 correctly labeling equilibrium P and Q for market; 1 for the firm graph (horizontal D or P curve); 1 applying MR = MC to find equilibrium quantity (MR must be logically consistent with demand curve) The market graph should have a downward-sloping demand curve and an upward-sloping supply curve with an equilibrium price and quantity clearly labeled. The firm graph should have a perfectly elastic (horizontal) demand curve at the equilibrium market price. The firm s profit-maximizing quantity is found at the intersection of this demand or marginal revenue curve with the firm s marginal cost curve. b. 1 pt.: showing the area of economic profit (above) for the firm (must use P, ATC, and q); The firm s profits are represented by the rectangle that has a height or (vertical distance) of P ATC multiplied by the firm s profitmaximizing output or q. c. 4 pts.: i. 2 pts.: 1 showing an increase in supply on market graph (resulting from entry of new firms); 1 showing both a lower P and a higher Q due to an increase in supply ii. 2 pts.: 1 downward shift in the firm s demand curve (P or MR or D); 1 for q (for firm) where P = min ATC for firm With profits being earned, new firms will enter the smoke alarm market. The market supply will increase (shift to the right) and the equilibrium price will fall and quantity will increase. As the market price falls, the firm has a downward shift in its horizontal demand curve. The process continues until price of output has fallen to the minimum of the average total cost of the firm.

9 d. 2 pts: 1 showing that Qs > Qm; 1 having 2 marginal benefit curves: one with and one without the positive externality With a positive consumption externality in the market for smoke alarms, the demand curve with marginal social benefits should lie above the demand curve with only marginal private benefits. Thus, the socially optimal output level will exceed the output level produced by an unregulated private market. e. 1 pt. for any of the following: subsidize sellers or buyers, mandatory smoke alarm system, or tax relief; To increase the market output to the socially optimal output, the government could subsidize the consumption or production of smoke alarms pts. a. 4 pts.: 1 correctly labeled graph w/ downward-sloping D curve and marginal revenue curve below demand; 1 indicating Q at MR = MC; 1 finding the appropriate P on the demand curve directly above MR = MC output; area of profit (must use P, ATC, and Q) For the monopolist, a correctly labeled graph should show a downward-sloping demand curve with a marginal revenue curve that lies below the demand curve. The monopolist s profit-maximizing output is found at the intersection of marginal revenue and marginal cost. The price is found on the demand curve, above the quantity produced. The firm s profits are represented by the rectangle that has a height (or vertical distance) of P ATC multiplied by the profit-maximizing output or Q.

10 b. 1 pt. the monopolist must lower its price on all units to sell additional quantities so MR < P; Marginal revenue is less than price since to sell additional units of output, the monopolist must lower price on all units of output sold. c. 2 pts.: 1 indicating correct area for consumer surplus; 1 correct area for deadweight loss; Consumer surplus is the area bounded vertically by the difference between the demand curve (willingness to pay) and monopolist s price over the number of units sold by the monopolist. The deadweight loss from monopoly is the combination of consumer and producer surplus that is lost when comparing the monopoly output to the output that would be produced under competitive conditions (where P MC) pts. a. 1 pt. definition: the additional revenue from hiring an additional worker or MRP = MP x MR or MRP = MP x P; The marginal revenue product of labor is the change in total revenue associated with the change in output following a unit change in the employment of labor; MRP of labor = MR (or P of output) x MPP of labor b. 4 pts.: 1 correctly labeled labor market graph showing equilibrium wage; 1 firm graph indicating downward-sloping demand (MRPl) curve; 1 horizontal labor supply curve for the firm; 1 showing quantity of labor for the firm at the intersection of labor supply and labor demand The perfectly competitive labor market will have a downward-sloping labor demand curve and an upward-sloping labor supply curve. There will be an equilibrium wage and quantity of labor. The firm will be a wage taker and have a perfectly elastic labor supply at the market wage rate. The firm s labor demand curve is its marginal revenue product of labor curve. Thus, the profit-maximizing firm will hire the amount of labor associated with the intersection of its marginal revenue product of labor curve and its horizontal labor supply curve. The firm will pay each unit of labor the market wage. c. 2 pts.: 1 wage rate for the firm remains constant at the original wage.; 1 the number of workers hired by XYZ increases b/c XYZ s MRP increases or labor demand curve shifts to the right.; With an increase in labor productivity that affects only Company XYZ there will be no perceptible change in labor market. The equilibrium wage stays the same. Company XYZ will have an outward shift in its marginal revenue product of labor (or labor demand) curve, leading to more employment at the unchanged market wage.

11 The table below shows total utility in utils that a utility-maximizing consumer receives from consuming two goods: apples and oranges. Apples Oranges Quantity Total utility Quantity Total Utility Assume that apples cost $1 each, oranges cost $2 each, and the consumer spends the entire income of $7 on apples and oranges. a. Using the concept of marginal utility per dollar spent, identify the combination of apples and oranges the consumer will purchase. Explain your reasoning. b. With the prices of apples and oranges remaining constant, assume that the consumer s income increases to $12. Identify each of the following. i. The combination of apples and oranges the consumer will now purchase. ii. The total utility the consumer will receive from consuming the combination in (i) c. with income remaining at $12, assume the price of oranges increases to $4 each. Identify each of the following. i. The combination of apples and oranges the consumer will now purchase. ii. The total utility the consumer will receive from consuming the combination in (i) Scoring and answer 3 6 pts Form B a. 2 pts.: 1 3 apples and 2 oranges; 1 --marginal analysis: equalization of MU/$ or 10/1 (apples) = 20/2 (oranges); student may not simply use the maximizing of total utility for the explanation.; The utilitymaximizing consumer will exhaust her income, purchasing quantities of each good such that for each commodity the marginal utility of the last unit purchased divided by the price of the commodity is equal. This consumer will purchase 3 apples and 2 oranges. The marginal utility per dollar of each commodity is equal: 10/$1 for apples and 20/$2 for oranges. (Marginal utility of 2 nd orange = 20 divided by price of $2; marginal utility of 3 rd apple is 10 divided by price of $1) b. 2 pts.: 1 4 apples and 4 oranges; = 125 utils; With the increase in income, the consumer will now purchase 4 apples and oranges and have 125 utils (50 from apples and 75 from oranges) c. 2 pts.: 1 4 apples and 2 oranges; = 100 utils: With the increase in the price of oranges, the consumer will now purchase 4 apples and 2 oranges and have 100 utils (50 from apples and 50 from oranges) 1. Assume that two firms are operating with identical cost schedules, but one firm is in a perfectly competitive industry, and the other is in a monopolistically competitive industry. a. Using two correctly labeled graphs, show the long-run equilibrium price and output levels for each of these two firms. b. Compare the long-run equilibrium price and output levels for these two firms. c. What level of economic profit will each firm earn in the long run? Why do these results occur? d. For each of the two firms at the equilibrium quantity, indicate whether the firm s demand curve is perfectly elastic, elastic, unit elastic, inelastic, or perfectly inelastic. How can you tell?

12 Scoring and answers 15 points a. 6 pts.: 1 each two graphs with appropriate cost curves; 1 each Q indicated for each firm where MR = MC; 1 each P for each firm read off the correct D curve at correct Q; see graphs above. The long-run equilibrium price and quantity are labeled Pm and Qm, for the monopolistically competitive firm and Pc and Qc for the perfectly competitive firm. b. 2 pts.: 1 P in perfect competition is lower than P in monopolistic competition; 1 Q in perfect competition is smaller than Q in monopolistic competition; The perfectly competitive firm has a lower price and a larger quantity of output than the monopolistically competitive firm. c. 3 pts.: 1 firm in perfect competition earns zero economic profit; 1 firm in monopolistic competition earns zero economic profit; 1 entry of new firms increases industry output, individual firm s output decreases, prices will fall to level of ATC; Each of these firms will earn zero economic profits in the long run. With no barriers to entry, the existence of positive economic profits or economic losses motivates the entry or exit of firms in and out of the industry, forcing prices to the level of average costs. d. 4 pts.: 1 for perfectly competitive firm, D is perfectly elastic; 1 b/c P is constant, the % change in P is 0; 1 for the monopolistically competitive firm, demand is elastic; MR is positive in the elastic portion of the D curve; Demand is perfectly elastic for the perfectly competitive firm because price is constant, making the percentage change in price zero for any change in quantity. For the monopolistically competitive firm, demand is elastic because MR is positive at Qm a. Assume that a profit-maximizing firm in a perfectly competitive industry is earning economic profits. For a given market price, draw a correctly labeled graph and show each of the following for a typical firm in this perfectly competitive industry. i. Marginal revenue ii. Output iii. Economic profits b. using the information given in (a), draw correctly labeled side-by-side graphs for the industry and a typical firm. i. Given the existence of economic profits of the typical firm, show on the graphs how the industry adjusts in the long run and explain the process that leads to the long-run equilibrium. ii. Show on the graphs each of the following for the industry and for the typical firm in long-run equilibrium: price, output c. Now assume that the government sets a price that is less than the equilibrium price but greater than average variable cost. Indicate how each of the following will change for the typical firm and explain why the change occurs. i. Marginal revenue ii. Level of output iii. Short-run total cost iv. Short-run total revenue 3. Sparkle Car Wash is a profit-maximizing firm with the following production information. Number of workers Number of Cars Washed Per Day 0 0

13 a. With which worker is marginal product maximized? b. Identify and define the economic principle that explains why marginal product eventually decreases. c. Explain why Sparkle would never hire the sixth worker. d. If Sparkle charges $6 for washing a car, what is the maximum daily wage that Sparkle would be willing to pay the fourth worker? Scoring and answers 1. The firm has a perfectly elastic (horizontal) marginal revenue curve that is equal to the market price. The firm produces the output level where marginal revenue equals marginal cost. The economic profit of the firm is the area bounded by the quantity produced multiplied by the difference between price and average total cost ( P ATC) at that output level. With economic profits, new firms will enter the industry. The market supply will shift outward with the entry of firms, and market price will fall. The process continues until a long-run equilibrium is established. At this equilibrium, the market price is equal to the minimum of the long-run average cost of the typical firm. Each firm produces where P=MR=MC, which is the level of output that corresponds to the minimum of the long-run average cost. The firm makes zero economic profits. A price control below the long-run equilibrium price but above the firm s average variable cost will result in short-run production. Since the price has fallen, the firm s marginal revenue falls. The firm s output level, where MR = MC, will also decrease. Since the firm is producing less output, total cost falls. Since both the firm s price and quantity have fallen, total revenue falls. a. 3 pts: 1 a horizontal MR curve; 1 show and indicate that output should be where MR = MC; 1 show the area of profit as the rectangle whose width is the distance between 0 and the equilibrium quantity and whose height is the distance between the P(AR) and ATC at that quantity. b. 5 pts. total: i. 3 pts.: 1 showing correctly side-by-side graphs of the firm and the market, both correctly labeled; 1 showing a market supply curve shifting out and a market price decreasing with this price being used in the firm graph; 1 explaining that w/ economic profits, more firms enter the market ii. 2 pts.: 1 showing the industry equilibrium price and quantity. Students can either use a vertical line from the x axis to the equilibrium pt. and one from the equilibrium pt. to the y axis (labeling each) or else they can mark the equilibrium pt. w/ a letter and somehow indicate that that pt. represents the equilibrium; 1 showing the long-run equilibrium price and quantity for the firm at the minimum ATC, indicating it via either of the methods discussed above

14 c. 4 pts.: i. 1 indicating that MR has fallen b/c P has been lowered ii. 1 indicate that output has fallen b/c MR = MC is at a lower q iii. 1 indicating that total costs fell b/c output fell iv. 1 indicating that price AND quantity fell Worker #3 has the highest marginal product (60 35 = 25 cars washed). With additional workers the marginal product falls. This is consistent with the Law of Diminishing Returns. That law states that as more units of a variable input (labor) are employed with a fixed input, output will eventually increase at a decreasing rate. The sixth worker would never be hired since the marginal product of that worker is negative (80 85 = -5 cars). A firm would never hire a unit of an input that reduces total output. The firm would be willing to pay the fourth worker as much as its marginal revenue product or $90 per day found by multiplying the price of a car wash by the number of cars washed by the fourth worker ($6 x 15 cars = $90 per day). 5 points total a. 1 3 rd worker b. 1 diminishing marginal returns; 1 definition of diminishing marginal returns that includes both variable and fixed inputs c. 1 negative marginal product for 6 th worker d $ Question 2 Assume that Countries A and B have equal amounts of resources and identical technologies. Country A can produce 100 bushels of wheat or 100 yards of cloth or any combination, as shown by the line XZ in the figure above. Country B can produce 100 bushels of wheat or 300 yards of cloth or any combination, as shown by the line XY in the figure below. Scoring and answer a. Which country has an absolute advantage in the production of wheat and which has an absolute advantage in the production of cloth? Explain how you determined your answer. b. Which country has a comparative advantage in the production of wheat and which has a comparative advantage in the production of cloth? Explain how you determined your answer. c. With specialization and trade, which country will import wheat? Explain why. d. Assume that the two countries trade, and that one bushel of wheat is exchanged for two yards of cloth. Explain why the country that imports wheat will gain from trade.

15 5 points total a. 1 pt with equal amounts of resources and identical technologies, each country can produce the same maximum quantity of wheat. Thus, neither country has an absolute advantage in wheat production. Country B has the absolute advantage in cloth production because it can produce more than country A.; wheat: neither country has an absolute advantage, identical outputs (w/ same resources) b. 2 pts: For Country A the opportunity cost of a bushel of wheat is 1 yard of cloth; for Country B, the opportunity cost of a bushel of wheat is 3 yards of cloth. Since Country A has the lower opportunity cost for producing wheat, Country A has comparative advantage in wheat production. Alternatively, Country B has the comparative advantage in the production of cloth.; 1 Country A has a comparative advantage in wheat; Country B in cloth; 1 show opportunity costs: Country A gives up 1 cloth for 1 wheat; Country B gives up 3 cloth for 1 wheat; relatively more expensive for Country B to produce wheat c. 1 pt. -- Given that comparative advantage is the basis for trade, Country B will specialize in the production of cloth, exporting cloth and importing wheat.; 1 country B will import wheat b/c it has a comparative advantage in cloth d. 1 pt. -- Country B will import wheat, exchanging 2 units of cloth for one unit of wheat; The country benefits from trade b/c if it produced wheat itself, a unit of wheat would be more expensive, costing 3 units of cloth.; For country B, via trade a unit of wheat costs only 2 units of cloth, while by domestic production a unit of wheat would cost 3 units of cloth. Trading allows B to consume more of both goods.