Quiz 2 Ec21 S2016 Solutions (1).pdf

Quiz 2 Ec21 S2016 Solutions (1).pdf - Economics 21 Spring...

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Page 1 of 6 Economics 21, Spring 2016 Prof. Luttmer Solutions to Quiz 2 1. Short Answer Questions (18 points) a. [4 points] Suppose the price elasticity of demand for Dartmouth Coach tickets is -0.5. At a price of $30, the quantity demanded is 20 tickets. At which price is the quantity demanded equal to 16? As always, show how you arrived at your answer. No credit for correct answer if you don’t show how you arrived at it. The price elasticity of demand, which is -0.5, is the percentage change in quantity demanded divided by the percentage change in price. The quantity demanded changes by -20% (from 20 to 16). Thus, the number by which 20% needs to be divided to yield -0.5 is 40%. Thus, the price increased by 40%. Adding 40% of 30 (=12) to 30 yields: 42. Thus, at a price of 42, the quantity demanded is 16. Note: please check your answer for making economic sense. A demand elasticity is a negative number. So if quantity goes down, price must increase. b. [3 points] Give the definition of the “compensating variation” of a policy. An individual’s Compensating Variation of a policy is the amount of income that needs to be taken away under that policy so that the individual is as well off as (=has the same utility as) under the previous policy. Thus, the CV is a measure of the welfare effect of the new policy relative to the old policy, and is positive whenever the new policy makes the person better off. c. [3 points] Give the definition of an inferior good. An inferior good is a good for which the quantity demanded falls as income rises (and relative prices stay the same). In other words, it is a good with a negative income elasticity of demand.
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Page 2 of 6 d. [4 points] Suppose a person consumes just two goods: 365 units of housing at a price of $80 per unit and 1200 units of food at price of $12 per unit. Assume both housing and food are normal goods. Suppose a new policy changes the price of food to $11.90 per unit and the price of housing to $81 per unit. Explain how this new policy affects the demand for food through the income effect and how its affects the demand for food through the substitution effect. Is the total effect of this new policy that the quantity of food demanded increases, stays exactly the same, decreases, or changes in an ambiguous direction? Explain your reasoning. The policy makes the person effectively poorer: the person becomes effectively 365*(81-80)=365 dollars poorer from the higher price of housing but only 1200*(12-11.9)=120 dollars richer from the lower price of food. 1 Hence, on net, the person is effectively poorer, and the income effect says that for a normal good this leads to a decrease in the quantity demanded. The relative price of food drops (because both food gets cheaper and housing more expensive). The substitution effect says that the quantity demanded increases for a good of which the relative price drops. Hence, for this policy, the income effect (decrease in quantity demanded) and the substitution effect (increase in quantity demanded) work in opposite directions. The total effect of this policy on the quantity demanded is therefore ambiguous.
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