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ECON 102 Tutorial: Week 6 Ayesha Ali www.lancaster.ac.uk/postgrad/alia10/econ102.html a.ali11@lancaster.ac.uk office hours: 8:00AM – 8:50AM tuesdays LUMS C85 Cost and Production Questions Key Concepts needed for these questions: Perfectly competitive firms are price takers, so for them MR = P. For all firms, profit is maximized at the quantity where MR = MC. When we want to understand how a firm makes entry/exit decisions, we use the shutdown conditions – these are different for the short run and the long-run: Short-run shutdown condition: A firm should shut down when MR < AVC. If the firm is perfectly competitive, this is when P < AVC. This can also be written as when TR < VC. Long-run shutdown condition: A firm should shut down when MR < ATC. If the firm is perfectly competitive, this is when P < ATC. This can also be written as when TR < TC or when profit < 0. Question 1: Ch. 5 Problem 2 A price-taking firm makes air conditioners. The market price of one of their new air conditioners is €120. Its total cost information is given in the table below. How many air conditioners should the firm Air conditioners Total cost per day (€ per day) 1 100 2 150 3 220 4 310 5 405 6 510 7 650 8 800 produce per day if its goal is to maximise its profit? Question 1: Ch. 5 Problem 2 A price-taking firm makes air conditioners. The market price of one of their new air conditioners is €120. Its total cost information is given in the table below. How many air conditioners should the firm produce per day if its goal is to maximise its profit? Air conditioners Total cost per day (€ per day) 1 100 2 150 3 220 4 310 5 405 6 7 8 510 650 800 Marginal Cost (€ per day) 50 70 90 95 Profit is maximized where MR = MC. Because this firm is a price taker, we know that MR = P. So what we want to find is at what quantity is MC = P? The MC for each of the first 6 air conditioners produced each day is less than €120 (MC<P), but the marginal cost of the 7th air conditioner is €140, (MC>P). 105 140 150 So the company should produce 6 air conditioners per day. Question 1: Ch. 5 Problem 3(a) The Paducah Slugger Company makes baseball bats out of lumber supplied to it by Acme Sporting Goods, which pays Paducah €10 for each finished bat. Paducah’s only factors of production are lathe operators and a small building with a lathe. The number of bats per day it produces depends on the number of employee-hours per day, as shown in the table below. If the wage is €15 per hour and Paducah’s daily fixed cost for the lathe and building is €60, what is the profit-maximising quantity of bats? Number of Number of Number of Number of bats per day employeebats per day employeehours per day hours per day 0 0 5 5 10 15 20 25 30 30 35 35 0 0 1 1 2 4 7 11 16 16 22 22 Total Revenue (€/day) TR = P*Q Total cost Profit Total labor (€/day) (€/day) cost (€/day) VC = wage* TC = FC + VC π=TR – TC # of employee hrs. Question 1: Ch. 5 Problem 3(a) The Paducah Slugger Company makes baseball bats out of lumber supplied to it by Acme Sporting Goods, which pays Paducah €10 for each finished bat. Paducah’s only factors of production are lathe operators and a small building with a lathe. The number of bats per day it produces depends on the number of employee-hours per day, as shown in the table below. If the wage is €15 per hour and Paducah’s daily fixed cost for the lathe and building is €60, what is the profit-maximising quantity of bats? As indicated by the entries in the last column of the table to the right, the profit-maximizing quantity of bats for Paducah is 20/day, which yields daily profit of €35. Number of Number of Total bats per day employee- Revenue hours per day (€/day) 0 5 10 15 20 25 30 35 0 1 2 4 7 11 16 22 0 50 100 150 200 250 300 350 Total labor cost (€/day) Total cost (€/day) Profit (€/day ) 0 15 30 60 105 165 240 330 60 75 90 120 165 225 300 390 -60 -25 10 30 35 25 0 -40 Question 1: Ch. 5 Problem 3(b) What would be the profit-maximising number of bats if the firm’s fixed cost were not €60 per day but only €30? Same quantity as in part a, but now profit is €65, or €30 more than before. Q Number of Total (bats/day) employee- Revenue hours per (€/day) day 0 0 0 1 5 50 2 10 100 4 15 150 7 20 200 11 25 250 16 30 300 22 35 350 Total labor Total cost cost (€/day) (€/day) 0 15 30 60 105 165 240 330 30 45 60 90 135 195 270 360 Profit (€/day) -30 5 40 60 65 55 30 -10 Question 1: Ch. 5 Problem 7 For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profitmaximising level of output and how much profit will this producer earn if the price of pizza is €2.50 per slice? Question 1: Ch. 5 Problem 7 For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profitmaximising level of output and how much profit will this producer earn if the price of pizza is €2.50 per slice? To answer this question, we use the same rule as we did in Ch. 5 Problem 2: For a perfectly competitive firm, profit is maximized where MC = P. This firm will sell 570 slices per day, the quantity for which P = MC. Its profit will be: π = (P-ATC)*Q π = (€2.50/slice - €1.40/slice)*(570 slices/day) π = €627/day. Question 1: Ch. 5 Problem 8 For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profit-maximising level of output and how much profit will this producer earn if the price of pizza is €0.80 per slice? Question 1: Ch. 5 Problem 8 For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profit-maximising level of output and how much profit will this producer earn if the price of pizza is €0.80 per slice? This firm will sell 360 slices per day, the quantity for which P = MC. Its profit will be: π = (P-ATC)*Q π = (€0.80/slice - €1.03/slice)*(360 slices/day) π = -€82.80/day. Question 1: Ch. 5 Problem 9 For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profit-maximising level of output and how much profit will this producer earn if the price of pizza is €0.50 per slice? Question 1: Ch. 5 Problem 9 For the pizza seller whose marginal, average variable and average total cost curves are shown in the diagram below, what is the profit-maximising level of output and how much profit will this producer earn if the price of pizza is €0.50 per slice? Because price is less than the minimum value of AVC, this producer will shut down in the short run. He will experience a loss equal to his fixed cost. Fixed cost is the difference between total cost and total variable cost. For Q = 260 slices/day, we know both ATC and AVC, so for that output level we can calculate: TC = ATC*Q = (260 slices/day)*(€1.18/slice) = €306.80/day VC = AVC*Q = (260 slices/day)*(€0.68/slice) = €176.80/day. So fixed cost, FC = TC - VC = €306.80/day - €176.80/day = €130/day. This producer’s profit is thus - €130/day. Perfect Competition Questions Question 1: Ch. 7 Problem 3(a) John Jones owns and manages a café whose annual revenue is €5,000. The annual expenses are as in the table below. Expense Labour Food and drink Electricity Vehicle lease Rent Interest on loan for equipment Calculate John’s annual accounting profit. € 2,000 500 100 150 500 1,000 John's accounting profit is his revenue minus his explicit costs, or €750 per year. Question 1: Ch. 7 Problem 3(b) John Jones owns and manages a café whose annual revenue is €5,000. The annual expenses are as in the table below. Expense Labour Food and drink Electricity Vehicle lease Rent Interest on loan for equipment € 2,000 500 100 150 500 1,000 John could earn €1,000 per year as a recycler of aluminium cans. However, he prefers to run the café. In fact, he would be willing to pay up to €275 per year to run the café rather than to recycle cans. Is the café making an economic profit? Should John stay in the business? Explain. Yes: his opportunity cost of his labour to run the café is €1,000 €275, or €725 per year. Adding this implicit cost to the explicit costs implies that the café is making an economic profit of €25 per year. And since €25>0, John should stay in business. Question 1: Ch. 7 Problem 3(c) John Jones owns and manages a café whose annual revenue is €5,000. The annual expenses are as in the table below. Expense Labour Food and drink Electricity Vehicle lease Rent Interest on loan for equipment € 2,000 500 100 150 500 1,000 Suppose the café’s revenues and expenses remain the same, but recyclers’ earnings rise to €1,100 per year. Is the café still making an economic profit? Explain. John's opportunity cost rises by €100, to €825 per year. The café is thus now making an economic loss of €75 per year. Question 1: Ch. 7 Problem 3(d) John Jones owns and manages a café whose annual revenue is €5,000. The annual expenses are as in the table below. Expense Labour Food and drink Electricity Vehicle lease Rent Interest on loan for equipment € 2,000 500 100 150 500 1,000 Suppose John had not had to get a €10,000 loan at an annual interest rate of 10 per cent to buy equipment, but instead had invested €10,000 of his own money in equipment. How would your answers to parts (a) and (b) change? The accounting profit would now be €1,750/yr. The answer to part b. would not change. If John had €10,000 of his own to invest in the café, he would forgo €1,000/yr in interest by not putting the money in a savings account. That amount is an opportunity cost that must be included when calculating economic profit. Question 1: Ch. 7 Problem 3(e) John Jones owns and manages a café whose annual revenue is €5,000. The annual expenses are as in the table below. Expense Labour Food and drink Electricity Vehicle lease Rent Interest on loan for equipment € 2,000 500 100 150 500 1,000 If John can earn €1,000 a year as a recycler, and he likes recycling just as well as running the café, how much additional revenue would the café have to collect each year to earn a normal profit? To earn a normal profit, the café would have to cover all its implicit and explicit costs. The opportunity cost of John's time is €1,000/yr, whereas the café's accounting profit is only €750/yr. Thus, the café would have to earn additional revenues of €250/yr to make a normal profit. Perfect Competition Q2(a) Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs. If the current market price of gizmos is $60, how many gizmos does Dave produce to maximize his profit? How much economic profit does Dave earn? Perfect Competition Q2(a) Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs. If the current market price of gizmos is $60, how many gizmos does Dave produce to maximize his profit? How much economic profit does Dave earn? We know that Dave’s marginal cost curve is MC(Q) = 4Q. Because Dave’s firm is in a perfectly competitive market, we know that it maximizes profit when MC(Q) = P. We can re-write this as: 4Q = 60 And solve for Q: Q = 15 To find Dave’s economic profit, we use the equation: π = TR – TC, where TR = P*Q and TC = FC + VC. When Dave produces Q = 15 units, his total variable costs are: VC(Q) = 2Q2 = 2(15)2 = 450 and his fixed costs are FC = 200. We can plug these in to the equation for economic profit: π = TR – TC π = P*Q – FC - VC π = 15*60 – 200 - 450 π = 900 – 650 π = 250 Perfect Competition Q2(b) Is the market price of $60 sustainable in the long run? Explain why or why not. No, this market price is not sustainable in the long run. Since firms in the industry are earning positive economic profit, new entrants will enter the industry; this will shift the supply curve to the right and drive the price down. Perfect Competition Q2(c) Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs. Write down the expression for Dave’s total costs The equation for Total Cost is: TC(Q) = FC + VC(Q) So Dave’s Total Cost is: TC(Q) = 200 + 2Q2 Perfect Competition Q2(d) Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs. In part (c), we found TC(Q) = 200 + 2Q2 Write down the expression for Dave’s average total cost Perfect Competition Q2(d) Dave owns a firm that produces and sells gizmos in a perfectly competitive market. His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has the same costs as Dave, and the costs I’ve described include both implicit and explicit costs. Write down the expression for Dave’s average total cost The equation for Average Total Cost is: ATC(Q) = TC(Q)/Q Plug in Dave’s total cost from part (c): ATC(Q) = (200 + 2Q2)/Q So Dave’s Average Total Cost is: ATC(Q) = 200/Q + 2Q Perfect Competition Q2(e) Solve for the long-run equilibrium price. We know that we have a perfectly competitive market. FC = $200/day, variable costs are VC(Q) = 2Q2 and Dave’s marginal cost curve is: MC(Q) = 4Q. In parts (c) and (d), we found TC = 200 + 2Q2 and ATC = 200/Q + 2Q. Perfect Competition Q2(e) Solve for the long-run equilibrium price. The long-run equilibrium price is the price where firms earn zero economic profit. This happens at the minimum of the ATC cost curve. To find the minimum of the ATC curve, recall that when MC = ATC, ATC is at its minimum. So, we can set MC(Q) = ATC(Q). We know that MC(Q) = 4Q, that was given in the problem. In part (d) we found ATC(Q) = 200/Q + 2Q. So let’s set MC(Q) = ATC(Q) Plugging in, we get: 4Q = 200/Q + 2Q 2Q = 200/Q 2Q2 = 200 Q2 = 100 Q = 10 So, ATC(Q) reaches its minimum when Q = 10. To find the value of ATC, we can plug in Q = 10 into ATC(Q) = 200/Q + 2Q. ATC(Q) = 200/10 + 2(10) = 40 Thus, the long-run equilibrium price is 40. Exam on Friday 50 minutes; 25 Questions: 16 from Rietzke, 9 from Peel. What to Revise: Practice MC Questions, Tutorial worksheets, Peel’s Maths Questions, Lecture Notes, and textbook chapters. Check your timetable for Exam time and location. Bring a pencil and erasor. No calculators, cell phones, or electronic translators will be allowed. (Paper versions of English-to-Other Language dictionaries will be allowed and checked by invigilators). Also, for next week, there will be a tutorial worksheet on Moodle, but no maths questions. Good luck and see you next week!