eco204_HW_3_solution

eco204_HW_3_solution - 1 s ECO 204 20082009 Ajaz Hussain HW...

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Unformatted text preview: 1 s ECO 204 20082009 Ajaz Hussain HW 3 Solutions Question 1 In lecture 3, we analyzed the effects of a public policy program that gave free education for exactly 12 years of education. Figure 1 depicts the private budget line and public budget point from that question: Figure 1 In this question, you will analyze two variations of that question: (a) "coupons" that can only be used for education (exactly like gift certificates that can be spent only a certain store) and (b) a cash subsidy. Assume consumer has "imperfect substitutes" preferences over education and everything else, which are each good goods. ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 2 Note: You may want to read BB p. 114118 after you attempt this question in their version of this question for housing instead of education they look at the case of someone who consumes less than a "mandated" level of housing. (a) Suppose the government gives everyone a coupon (voucher) which can be used to obtain the up to 12 years of education for free. Analyze the impact of this policy on optimal choice, "happiness" and education levels. Note: in this question, the consumer will have the option of 12 years of education for free and if she wants more than 12 years of education to pay for additional years of schooling. In the lecture question you had to either go to free public schools for 12 years or go to private schooling for any number of years. Answer: The coupon is an education "gift" allowing the recipient to get 12 years of education absolutely free. Let education be on the x axis and everything else on the y axis. The slope of the budget line is: P1/P2 = Peducation/Pelse. The coupon makes the first 12 years of education freel; thus, the for the first 12 years, the slope of the budget line is 0. For any education beyond 12 years, the slope will Peducation/Pelse . In essence, the budget line shifts out, but leaves the maximum amount of other goods that can be purchased unchanged. The shift is almost as if the consumer has a higher income, except that she cannot spend the extra income on everything else. Figure 2 depicts the initial and new budget constraints: Figure 2 As with the analysis in lecture 3, the impact of the program depends on preferences and initial choices. Three cases are depicted in Figures 3 through 5. ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 3 Figure 3 In Figure 3, the consumer avails herself of the voucher program by studying more and buying more of everything else here, everything else and education are normal goods. At the initial and new optimal choice, her MRS = slope of the budget line and she is happier than before. Figure 4 In Figure 4, the consumer avails herself of the voucher program by buying more of everything else but studying the same number of years as before. Here, everything is a normal good but education is neither a normal nor an inferior good. At the initial and new optimal choice, her MRS = slope of the budget line and she is happier than before. You should be able to easily draw a case where the consumer will study less when there is a voucher program (the case where everything else is a normal good and education is an inferior good). ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 4 Figure 5 In Figure 5, the consumer avails herself of the voucher program by studying more and buying more of everything else. At the initial optimal choice her MRS = slope of the budget line but at the new optimal choice MRS slope of the budget line. She is happier than before. It appears from these three cases, that the voucher program results in varying effects on education (some study more, some less, some same) but all seem to result in more happiness. This is in contrast to the public policy analyzed in lecture 3 where it was possible that switching to public education could potentially make some people less happy. Why is this not happening here? The answer is that the voucher makes available (education, else) choices that were previously unavailable to the consumer. Since the voucher makes more of education and else available by the more is better assumption this makes the consumer happier. Although she may consume less of one good, she won't consume less of both goods (from lecture 4, recall that with "more is better" preferences not every good can be inferior). (b) Suppose the government gives a cash payment guaranteeing 12 years of education which the consumer can spend however she wishes. Analyze the impact of this policy on optimal choice, "happiness" and education levels. In particular, compare the optimal choices in the coupon versus subsidy programs. Answer: The cash subsidy, denoted S, is tantamount to boosting consumer income from Y to Y + S, shifting the budget line out by S (Figure 6). Notice, the cash subsidy makes available more (education, else) combinations than the voucher program. ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 5 Figure 6 The impact on optimal choice and happiness depends on preferences. Here are some interesting cases: Figure 7 In Figure 7, with the cash subsidy, the consumer is made better off; she consumes more education and everything else. But her choice with the cash subsidy is identical to the choice under the voucher program, despite the fact that the subsidy program makes more bundles available than the voucher program. Next, in Figure 8, with the cash subsidy, the consumer is made better off; she consumes more education and everything else and her choice with the cash subsidy is different from the choice ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 6 under the voucher program. Figure 8 In this case, the person is happier with the cash subsidy than the voucher program. Compared to the initial level of education, the subsidy program also results in more education but less than the voucher program. Figure 9 depicts the case of someone who is happier with the subsidy program but consumes less education for her, education is an inferior good. Figure 9 ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 7 Question 2 You are the proud owner of McCurryHurry, a fast food chain specializing in South Asian fast food cooking (they give you the ingredients and tell you to go home and cook it yourself). The parent corporation McCurryHurry, WeTakeYourMoneyinaHurry has conducted market research across Canada and has found that the storelevel demand for McCurryHurry's best selling product, Chicken Brr! Yani (it's Canada after all!) is: Q = 400 1,200 P + 0.8 A + 0.55 Pop + 800 Po Q = Sales of Chicken Brr! Yani per week, P = Price of Chicken Brr! Yani, A = advertising per week, Pop = Local population in thousands, Po = Price of other goods. Currently: P = $1.50, A = $1,000, Pop = 40, Po = $1. (a) Are the "other goods" substitutes for or complements to Chicken Brr! Yani!? Answer: The coefficient on price of other goods is positive: this means as price of other goods increases, quantity of Chicken Brr! Yani increases. This can only be if the other goods are a substitute for Chicken Brr! Yani: Price of other goods increases Quantity of other goods decreases Consumers "switch" to Chicken Brr! Yani Quantity of Chicken Brr! Yani increases (b) How many Chicken Brr! Yani's will each store sell per week? Answer: Q = 400 1,200 P + 0.8 A + 55 Pop + 800 Po Q = 400 1,200(1.50) + 0.8(1,000) + 55(40) + 800(1) = 2,400 (c) Estimate the price elasticity for Chicken Brr! Yani. Any recommendations? Answer: Because there is no initial and final price/quantity we must use point E: E = % change in Q/% change in P E = (dQ/dP)(P/Q) = (1,200) (1.50/2400) = 0.75 ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 8 The demand curve is linear and because |E| < 1, we recommend that prices should be raised to increase revenues. If we want to maximize revenues, prices should be raised until |E| = 1. For profits prices should be raised so that |E| > 1 (precisely at which price point is something we do next semester). (d) Estimate the advertising elasticity for Chicken Brr! Yani. Any recommendations? Answer: The definition is: % change in Q/% change in A. Again, we use point elasticity: E = (dQ/dA)(A/Q) = 0.8(1000)/(2400) = 0.33. This implies that a 1% increase in advertising budget raises sales by 0.33%. If prices are constant, then this implies that revenues will increase by 0.33% (remember: % change in R = % change in P + % change in Q). (e) Derive the demand curve for your store Answer: A demand curve plots P vs. Q, ceteris paribus. Thus, we need to hold A, Pop, Po constant: Q = 400 1,200(I) + 0.8(1,000) + 55(40) + 800(1) Q = 4,200 1,200P 1,200 P = 4,200 Q P = 4,200/1,200 (1/ 1,200) Q = 3.5 1/1,200 Q Question 3 After graduation you're hired by the "Say No to Puffing" Foundation, a Canadian nonprofit organization which aims to prevent smoking. You collect data on the annual consumption (Q) and price (P) of cigarettes, annual expenditure on advertising (A) and per capita income (Y). You estimate a constant elasticity model and obtain: ln(Q) = 2.55 0.29 ln(P) 0.09 ln(Y) + 0.08 ln(A) 0.1 W ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 9 Where W = 1 for years after 1953, when the American Cancer Society linked smoking to cancer. (a) Write the model in the "constant elasticity" demand function form. Answer: Review your class notes where you'll see we did the simple constant elasticity demand function Q = (constant 1) Pconstant 2 . We showed this can be written as ln(Q) = ln(constant 1) constant 2 ln(P). In this question we're given the ln form and asked to write the original constant elasticity model: ln(Q) = 2.55 0.29 ln(P) 0.09 ln(Y) + 0.08 ln(A) 0.1 W ln(Q) = ln(e2.55) + ln(P) 0.29 + ln(Y) 0.09 + ln(A) 0.08 + ln(e0.1W) ln(Q) = ln(e2.55P 0.29 Y 0.09 A0.08 e0.1W) Q = e2.55P 0.29 Y 0.09 A0.08 e0.1W If you don't understand these steps, you should review the properties of logs. (b) What is the price elasticity? Answer: Because this is the constant elasticity demand function, the price elasticity is simply the coefficient of ln(P) in: ln(Q) = 2.55 0.29 ln(P) 0.09 ln(Y) + 0.08 ln(A) 0.1 W or, alternatively, the power of P in: Q = e2.55P 0.29 Y 0.09 A0.08 e0.1W . E = 0.29 Because |E| < 1, the price elasticity is inelastic--i.e. a 1% change in price leads to a less than 1% change in quantity. Note that the industry wide E generally tend to be inelastic because fewer alternatives are available to the industry as a whole. Put simply, if a single company raises prices, consumers can "switch" to another company's product. Thus, company E tends to be elastic. But if an entire industry raises prices then consumers won't have many substitutes that they can switch to (at least in the short run). Thus, industry E tends to be inelastic. ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto 10 (c) What is the income elasticity? Are cigarettes a normal good? Answer: By the same logic in part (b), income E = 0.09, which being negative implies that cigarettes are an inferior good. (d) What is the advertising elasticity? Answer: Advertising E = 0.08. This means, a 1% increase in A leads to a 0.08% increase in Q. (e) Interpret the coefficient on W. Ceteris paribus what was the impact of the cancer report on cigarette sales? Answer: The coefficient on W is = 0.1. To see what this means, take the derivatives of ln(Q) with respect to W: dln(Q)/dW = 0.1 Now remember that dln(x)100 = (dx/x)100 = % change in x, and so: % change in Q/dW = 0.1 % change in Q = 0.1(dW)100 = 10% dW = 1 for all years after 1953, This means that ceteris paribus the report on cancer (released in 1953) reduced cigarette sales by 10%. ECO 204, 20082009. Ajaz Hussain. Department of Economics, University of Toronto ...
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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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