University of Toronto Department of Economics ECO101: Principles of Microeconomics Robert Gazzale, PhD Term Test 2 2018: Gazzale Regular Solutions: Full While you wait for the test to start, please fill in the information below. DO NOT OPEN THIS TEST BOOKLET UNTIL INSTRUCTED. UofT email: Code of Conduct With my signature below, I attest to understanding the University of Toronto’s Code of Behaviour on Academic Matters, and promise my adherence for the good of my community. Signature: 20181119GazzaleRegular Term Test 2: Solutions: Full 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. General Instructions 105 minutes. 106 marks. Allocate your time wisely! OTHER test booklet: Multiple choice questions. 53 marks. THIS test booklet: Short answer and calculation questions. 53 marks. THIS test booklet: Record multiple-choice answers on last page. Aids allowed: a non-graphing, non-programmable calculator; a straight edge (i.e., ruler). For True, False or Uncertain questions, all marks are earned for the explanation. Show your work. No work, no partial marks. When explanations are needed, be clear, accurate, and concise. Avoid the temptation to write too much. The final page is blank. If you need to continue an answer on this page, you must write “Continued on final page” in the question’s answer space. Unless otherwise stated, assume quantities need not be integers. I. [25 Marks] TFU means “True, False or Uncertain?”. All marks are earned for the explanation. (1) [5 Marks] You are organizing a charity concert. You must sell each ticket at the same price. You will donate the difference between total revenues and total costs to the charity. Drake has agreed to perform, for free! You rented the 19,900-seat Scotiabank Arena, for $1! Given the downwardsloping linear demand curve for tickets, you correctly calculate that $500 per ticket maximizes the charitable donation. Then, you then learn that that you have to pay a $5 per-attendee “security charge”. TFU: $500 still maximizes the charitable donation. Suggested Solution: Uncertain. It is true when you M R = M C at a quantity greater than 19,900. (The is the same as M R > M C at 19,900. If M C = 0, it is the same as demand is elastic at 19,900). In this case, you find the price where Qd = 19, 900, and your supply is perfectly inelastic at this price. Because your supply is perfectly inelastic, you bear the full incidence of the tax. False when M R = M C at a quantity less than 19,900. You do not plan on selling all the tickets. In this case, you are selling a quantity were M R = M C. This increase in marginal cost causes you to reduce quantity and increase price. (With a linear demand curve, the increase in price is exactly $2.50.) (2) [5 Marks] Assume a perfectly competitive market where quantities must be integers and supply and demand schedules are depicted in the following table. Q MWTP MC 1 $21 $5 2 $18 $8 3 $16 $10 4 $14 $12 5 $12 $14 6 $10 $16 7 $8 $18 TFU: If the equilibrium price without government intervention is $13, then a price ceiling at $11 increases consumer surplus by $5. Suggested Solution: Uncertain. Originally, four units are transacted, with the four highest MWTP getting the item. With the ceiling at P = $11, only three units are supplied and thus only three units are transacted. IF these three items go to the highest MWTP, then the increase in CS is $5. The three highest pay $2 less, for a total increase of $6, but consumer four no longer transacts and we thus lose the $1 in surplus she got. HOWEVER, there are five consumers willing to pay at least $11, and consumer surplus will be reduced if either four or five gets an item (i.e., if the items do not go to the highest WTP consumers). 20181119GazzaleRegular Term Test 2: Solutions: Full (3) [5 Marks] Assume quantities need not be integers. I am offering you the opportunity to be the only seller of silent velcro in Toronto, where per-period demand is P (Q) = 20 − Q. If you accept, you pay me a fixed cost of $30 per period and $10 for each unit you sell. These are your only costs. TFU: You should accept the offer to be the only seller of silent velcro in Toronto. Suggested Solution: Uncertain. If you are constrained to charging the same price for each unit, you charge $15, earning $5 on each of 5 units. This is not sufficient to cover your fixed costs. However, if you can price discriminate, you can increase PS. At best, you engage in first-degree price-discrimination and earn $50 in PS each period. In this case, you should accept. Note: For full marks, you need to establish that it is possible for price discrimination to result in at least $30 in surplus. After all, the statement would be false if the fixed cost was $100. (4) [5 Marks] You are a monopolist constrained to charging the same price for each unit who faces a standard linear demand curve. You have correctly calculated that your profit maximizing price is $10 and you would sell 1000 units at this price. TFU: A price ceiling set at P = $9 reduces your short-run profits by $1000. Suggested Solution: False. Your short-run profits (i.e., fixed costs minus producer surplus) decrease by less than $100. For the 1000 items you would have sold at P = $10, you lose $1 in surplus on each for a reduction of $1000. However, you will sell more units at P = $9, and you make some P S on each of these extra units. Note: You lost marks if you wrote that this could increase profits. As producer surplus, and thus profits, are maximized at P = $10, profits must be less at any other price. (5) [5 Marks] Assume labour must be purchased in integer quantities at $20 per unit. You have incurred a fixed cost equal to $1000, and each item you produce requires $9 in materials and some labour. Currently, you produce and sell 1002 units at $20 each. TFU: If the marginal product of the last worker you hired was 2, then hiring this worker increased your profits. Suggested Solution: Uncertain. By hiring this worker, you increased your costs by $38: $20 in labour and $9 × 2 = $12 in materials. If you are a firm in a perfectly competitive market, then you can sell as much as you want at the market price of $20 for a benefit of $40. As the marginal benefit was greater than the marginal cost, this increased your producer surplus and thus your profit. However, if your firm has market power, we have to consider the price effect: you would have gotten a slightly higher price had you not hired the last worker and only sold 1000. II. [12 Marks] Kipchoge Enterprises (KE) provides coaching services. Eliud is both the owner and only employee (i.e., coach). Each period, KE pays $1550 in rent, and faces per-period demand P (Q) = M W T P (Q) = 120 − Q, where Q is the number of hours of coaching Eliud provides. By law, coaches must be paid exactly $20 per hour. (While KE must pay Eliud $20 per hour, KE can charge customers whatever it likes.) (1) [4 Marks] If KE had to charge the same price for each hour of coaching services and KE maximized accounting profits, what are KE’s accounting profits? 20181119GazzaleRegular Term Test 2: Solutions: Full Suggested Solution: The math: M R(Q∗M ) = M C(Q∗M ) 120 − 120 − 2Q∗M 2Q∗M = M C(Q∗M ) = $20 100 = profit maximization twice-as-steep rule substituting 2Q∗M Q∗M = $50 P (Q∗M ) = 120 − Q∗M ∗ PM ∗ πM solving for price = 120 − 50 = $70 ∗ = P SM −F = ($70 − $20) × 50 − $1550 = $2500 − $1550 = $950 Because with have linear demand an constant M C, you could have saved a little math if you remembered that the profit maximizing price if halfway between the vertical intercept of the = $70. demand curve and the marginal cost: P m = 120+20 2 (2) [3 Marks] You find out that every hour Eliud worked for his firm, he could have either worked for Keitany Consulting at $40 per hour or Uber at $15 per hour. Concisely explain to Eliud (who has never heard of the economics terms you now know) why accounting profits are not the true measure of KE’s profitability. Suggested Solution: A general answer: We want to do anything where the benefit is greater than the cost. The “firm” is choosing the number of hours assuming the cost is $20. The true cost, however, is $40 per hour, as every hour he works for KE he is giving up $40. If you went the example way: Eliud keeps every extra dollar generated whether as salary or profit. As hour of consulting that generates $30 in revenues seems profitable as it is greater than the $20, but is not profitable because Eliud gave up $40 to generate the $30. Note: For full marks, you must make it clear that the true cost to Eliud of using his time for his business is $40. (3) [5 Marks] KE’s current lease is complete and Eliud now has the choice whether commit to paying $1550 per-period in rent. Given his costs, the demand for Eliud’s coaching services (P (Q) = M W T P (Q) = 120 − Q), and the fact that KE must charge the same price for each hour, should KE sign a new lease? (Full marks are given for the explanation.) Suggested Solution: If he continues to provide 50 hours per month, his true producer surplus is ($70 − $40) × 50 = $1500, which means that his business would not be profitable as his fixed cost is $1550. However, to find the number of hours maximizing his economic profits, he should use his true marginal cost of $40 per hour. P m = 120+40 = $80. Qm = 40. P S = ($80 − $40) × 40 = $1600. 2 π = 1600 − 1550 = 50. So yes, the business is profitable and he should sign the lease. III. [16 Marks] Assume continuous quantities. Coffee roasting is perfectly competitive in Boblandia. All firms face the same costs. To roast coffee, a firm must rent one coffee roasting machine at 50 Bobos per period, and then incurs a marginal cost for each pound roasted. In particular, to roast qi pounds, 20181119GazzaleRegular Term Test 2: Solutions: Full a firm’s costs are: M C(qi ) = 10 + qi T C(qi ) = 50 + 10qi + marginal cost qi2 2 total cost (1) [2 Marks] Labelling any and all lines or curves, in the graph below clearly identify PBE , the price at which a firm earns zero economic profits in the short run. (Hint: You need two “curves”. The curves need to be qualitatively correct. They do not need to be numerically correct.) Suggested Solution: Your graph will have a U-shaped AT C, will have the upward-sloping portion of the M C intersect AT C at AT Cmin , and will show that PBE is the minimum value of the AT C. Note: The M C in this question is everywhere upward sloping. (2) [3 Marks] If the price is PBE , clearly but concisely explain how your graph shows economic profits are zero. Suggested Solution: The behavioural rule is to keep increasing output as long as MB (the market price, in a competitive market) is at least as large as marginal cost. This means finding the quantity (qi∗ ) where MC=P. At PBE , ATC=P, meaning total revenue (PBE × qi∗ ) equals total costs (AT C(qi∗ ) × qi∗ ). Note: For full marks, you must be clear that M C determines your quantity. That is, when the price is where AT C = M C (i.e., the minimum of the ATC), you stop at the quantity where P = AT C. 20181119GazzaleRegular Term Test 2: Solutions: Full M C(qi ) = 10 + qi T C(qi ) = 50 + 10qi + marginal cost qi2 2 total cost (3) [4 Marks] Solve for the price at which firms in the market earn zero economic profits. Suggested Solution: We need to find the minimum of the ATC curve. To find AT C(qi ), take T C(qi ) and divide by qi . The minimum of the ATC occurs at the qi where AT C = M C.1 AT C(qi ) = M C(qi ) q 50 + 10 + = 10 + qi qi 2 50 q + = qi qi 2 50 q = qi 2 100 = qi2 at AT Cmin substituting qi = 10 To find the value of ATC at AT Cmin , substitute qi = 10 into either MC or ATC. PBE = 10+10 = $20 (4) [4 Marks] Market demand is Qd (P ) = 1000−10P . If there are currently 50 firms in the market, ∗ )? what is the market price (PSR Suggested Solution: In a competitive market, as the market price is a firm’s marginal benefit of producing, the firm chooses the quantity where M C = P , this given a price P, it chooses qi such that P = 10 + qi . To find market supply, we need to sum each firm’s production at each price. This means we need qi as a function of price. We thus invert P = 10 + qi to get qi (P ) = P − 10. As all firms are identical, market supply as a function of price is Qs (P ) = 50 × qi (P ) = 50(P − 10). As equilibrium equates quantities supplied and demanded: Qd (P ∗ ) = Qs (P ∗ ) ∗ ∗ 1000 − 10P = 50(P − 10) P∗ 20 − = P ∗ − 10 5 100 − P ∗ = 5P ∗ − 50 equilibrium condition substituting 150 = 6P ∗ P ∗ = 25 1 If you are a calculus freak, you could take the derivative of the AT C function with respect to qi and set it equal to zero, then solve for qi . 20181119GazzaleRegular Term Test 2: Solutions: Full (5) [3 Marks] Your firm rents coffee roasting machines to firms that roast coffee. Given the short-run with 50 coffee-roasting firms, explain whether you expect demand for coffee roasting machines to increase or decrease. (Note: It is possible to get full marks for this question even if you did none of the previous questions.) Suggested Solution: You can get full marks even if you did not calculate whether the current price is above or below the break-even price. ∗ >P The general answer If PSR BE , then the firms in the market are earning positive economic ∗ < profits. This induces entry, which increases demand for coffee roasting machines. If PSR PBE , then the firms in the market are earning negative economic profits. This induces exit, which decreases demand for coffee roasting machines. ∗ >P If you calculated prices PSR BE , . . . Importantly, if you miscalculated prices but your logic for this question is correct, you got full marks. INTENTIONALLY LEFT BLANK. WE WILL LOOK AT THIS PAGE ONLY IF YOUR ANSWER TO A QUESTION REFERS US TO THIS PAGE. 20181119GazzaleRegular Term Test 2: Solutions: Full