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hw 2 Soln

# hw 2 Soln - Homework 2 Sample Solution 1a According to...

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Unformatted text preview: Homework 2 Sample Solution 1a. According to Besanko and Braeutigam, why are brand-level and market-level elasticities of demand different? The difference “reflects the impact of substitution possibilities” that are more widely available at the brand level than at the market level. See page 45 of the text. b. Suppose the brand-level and market-level elasticities of demand are known. If we know the relevant values are — 0.3 and — 3.0, which of those values is likely to be the brand—level elasticity and which is likely to be the market-level elasticity? Explain. Whatever value the market—level elasticity takes, because of the substitution possibilities between brands when only a single brand changes price, the brand—level elasticity is likely to be larger in absolute value (i .e., the brand level demand is likely to be more responsive to own- brand price changes alone). Thus the brand-level elasticity is likely to be — 3.0 and the market- level elasticity is likely to be — 0.3. 2. As estimated by Buschena and Perloff (1991), the demand function for coconut oil is Q = 1,200 — 9.5p +16.2pp + 021’ where Q is the quantity of coconut oil demanded in thousands of metric tons per year, ,0 is the price of coconut oil in cents per pound, 17,, is the price of palm oil in cents per pound, and Yis average consumer income in thousands of dollars per year. a. What is the equation of the demand curve for coconut oil when the price of palm oil is 5 cents per pound and average income is 55 thousand dollars per year? Q = 1,200 - 9.5p +16.2pp + 0.2Y = 1,200 — 9.5;) + 16.2(5)+ 0.2(55) = 1,292 — 9.5;) so [3019) = 1,292 — 9.5p is the equation for 0 s p s 136 2 1292/95 (where the formula provides a non-negative answer). (For p > 136, D(p) = 0.) b. Carefully graph the demand curve for coconut oil found in 2a. Be sure to label the axes and the intercepts. Make your diagram as accurate as possible. P Cents/lb 1292/9 .5 = 136 Q = D(p) = 1,292 —9.5p forp £- 136 AndD(p)=0forp>136 Q 1292 1000 metric tons/year c. How does the demand curve shift if the price of palm oil increases from 5 cents to 15 cents per pound? - Q = 1,200 - 9.5p +16.2pp + 021’ = 1,200 — 9.5p + 16.2(15)+ 0.2(55) = 1 ,454 — 9.5p so D*(p) = 1,454 — 9.5p is the new equation for p 5 1454195 z 153. The demand curve has shifted to the right by 162 = 1454 — 1292 (thousand metric tons per year). For each price with positive demand (at the original palm oil price), the new quantity demanded is 162 (thousand metric tons per year) more than the quantity demanded with the original demand curve. (For prices between 136 and 1454/9.5, D(p) = 0 but D*(p) = 1,454 —- 9.5;) > 0. The difference in the two versions of demand is positive, but less than 162.) d. By how much must the price of coconut oil decrease in order to have the quantity demanded increase by 30 thousand metric tons per year? Does your answer depend on whether you use the demand curve from Part (a) instead of from Part (c) (after the change in the price of palm oil)? Explain why or why not. Starting from a price at which the quantity demanded is strictly positive, the answer does not depend on whether Part (a) or Part (c) is used because the question is about movement along a demand curve and both versions have the same slope. From the equation for demand, the relation between changes in price and changes in quantity demanded is AQ = — 9.5Ap, and we need AQ = + 30. Thus 30 = — 9.5Ap or Ap = —— 30/95 2 — 3.2 and the price of coconut oil must decrease by approximately 3 .2 cents per pound. (T his works as long as the starting price was at least 3.2 cents per pound.) ...
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