eco204_HW_9_solution

eco204_HW_9_solution - University of Toronto Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain ECO 204 2008‐2009 Ajaz Hussain HW 9 Solutions Question 1 In the 1970s, Coca‐Cola (the number 1 global brand) used sugar in its secret formula. Rising sugar prices and changing consumer tastes away from high calorie drinks to low calorie drinks, forced Coca‐Cola to tinker with its formula. In particular, Coca‐Cola considered switching from sugar to corn fructose syrup. In all questions, put fructose on the x‐axis and sugar on the y‐axis. (a) Coca‐Cola initially could not develop a new formula for Coke that used fructose as an input while maintaining the “taste” of Coke. What do Coke’s iso‐quants look like? How much of sugar and fructose will Coke use in its products? Answer: Your understanding of consumer choice will help in this question of producer choice. Coke is unable to formulate its secret recipe to use fructose and maintain the taste of the product. This implies, no matter how much fructose is used, or no matter how cheap fructose is, Coke will only use sugar in its products. Think of a similar question in consumer choice where a person likes martinis but not sushi. The iso quants are depicted in Figure 1. 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain Figure 1 Observe that regardless of the price of sugar or fructose, cost minimization involves using zero fructose and some sugar. Figure 2 shows the optimal choice of inputs for a target output of q and uniform prices for fructose and sugar: Figure 2 (b) Coca‐Cola figured out a way to mix sugar and fructose and maintain Coke’s taste but had to still use some sugar. What did Coke’s iso‐quants look like? Hint: there is more than one answer. Also, at this time, Coke used a 50‐50 combination of sugar and fructose in its products—show this on your diagram. 2 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain Answer: If Coke manages to tweak the formula, so that fructose and sugar can be mixed but the use of sugar not be eliminated, one possible iso‐quant is depicted in Figure 3: Figure 3 The iso‐quant does not touch the x‐axis, which implies the technology must use some sugar. The iso‐cost in Figure 3 shows that equal amounts of sugar and fructose. With different fructose and sugar prices Coke‐‐ despite the fact it can mix fructose and sugar‐‐ may still use only sugar (see Figure 4). Figure 4 3 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain (c) Fructose prices continued to drop and Coca‐Cola got better at tweaking its formula to incorporate fructose. By the later 70s, Coca‐Cola was able to mix sugar and fructose and using only fructose in its products. Show this on an iso‐quant/iso‐cost diagram. Answer: If Coke is able to mix fructose and sugar and uses only fructose, then some possible iso‐quant/iso‐cost are depicted in Figures 5 and 6: Figure 5 Figure 6 4 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain Question 2 After quitting his job as a professor, Hu‐sea‐n becomes a fishmonger. Each morning Hu‐sea‐n’s cousin Ho‐sea‐us‐‐ a fisherman‐‐ drops off his daily catch. Any unsold fish is discarded. (a) What is Hu‐sea‐n’s MC of selling a fish? Think carefullyon the meaning of “MC”. Answer: MC is dC/dq. Put simply it is additional (variable) cost of an additional unit. You should think carefully on the meaning of “additional output”. If you were Hu‐sea‐us the fisherman, then an additional unit means catching another fish, for which there is a probably a cost ‐‐ think fuel, coffee, bait etc. Now think about Hu‐sea‐n the fishmonger. For him an additional unit is another fish from his stock of fresh fish. The MC of selling another fish from his stock is most likely $0 (or close to $0). But the MC of selling more than the daily catch is inifinity‐‐ after all, once he has the stock of fish delivered he cannot add a fish; i.e., the cost of adding another fish is prohibitive. Thus, Hu‐ sea‐n’s (not Ho‐sea‐us!) MC curve is flat from [0, Daily catch] and infinity onwards as shown in Figure 7. Figure 7 (b) Suppose Hu‐sea‐n sells fish in a perfectly competitive market. Show that he would always sell its entire daily catch. Answer: If Hu‐sea‐n sells fish into a competitive market, he is a price taker. Thus, his demand curve is flat. From ECO 100, his MR curve is identical to the demand curve. Here is why: in perfect competition the price is a constant (given from the market). Thus: P = constant. Hence: 5 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain R = p q = p constant → MR = dR/dq = constant Thus the demand and MR curves are coincidental. Hu‐sea‐n will sell the profit maximizing number of fish (MR = MC) as in Figure 8. There, the only output at which MR = MC is the “daily catch”. Hence, he will always sell the entire stock of fish. Figure 8 (c) Suppose Hu‐sea‐n sells fish is a monopolist. Show that he would not always sell its entire daily catch. Answer: With Hu‐sea‐n as a monopolist, his demand curve‐‐ identical to the market demand curve‐‐ is downward sloping. From ECO 100, so will the MR curve (which, if the demand curve is linear, will have the same intercept and twice the slope of the demand curve). Depending on the demand curve (“high” or “low”), the MR curve may be “high” or “low”. Hu‐sea‐n may therefore sell the entire catch (when MR cuts the MC curve), or, sell less than the daily catch. See Figures 9 and 10 respectively. In Figure 9, MR = MC at the daily catch ‐‐ all fish will be sold. In Figure 10, MR = MC below the daily catch so that there will be some unsold fish. Thank goodness Hu‐sea‐n throws away unsold fish. Not like other fishmongers who sell unsold fish to sushi restaurants on Bloor Street (yes, true story). 6 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain Figure 9 Figure 10 Question 3 Pablo Picasso was a prolific artist. He created hundreds of drawings, paintings, sculptures, drawings and sketches. (a) What effect does the existence of a large body of wok have on the monetary value of individual pieces of his art? Answer: If the price of Picasso’s works is determined by market demand for and supply of his 7 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain works, then a “large body of work” is tantamount to shifting the supply curve out and thus depressing the price of Picasso works. (b) Might his heirs suffer from being bequeathed too many of hisworks? If you were the financial adviser to his descendants, what advice would you proffer? Answer: Picasso’s heirs are interested in maximizing revenues from sales of Picasso’s art. If the demand curve is inelastic (i.e. |E| < 1) then a lower price will decrease revenues. To keep prices high, Picasso’s heirs should release the works slowly over time. It would be a big mistake to sell the works at once. 8 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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