Homework Clinic
Social Science Clinic => Economics => Microeconomics => Topic started by: cookcarl on May 24, 2019
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The table gives the total utility Jamal derives from the consumption of eclairs and cream puffs. Jamal has $12 to spend on these two confectionery goods. The price of an eclair is $3 and the price of a cream puff is $1.50.
a. Jamal's budget is $12. In order for Jamal to maximize his utility, how many eclairs and cream puffs should he buy?
b. Suppose the price of an eclair increase to $6. Jamal's income does not change and neither does the price of a cream puff. What combination of eclairs and cream puffs will Jamal buy now?
c. Using your answers to parts (a) and (b), derive two points on Jamal's demand curve for eclairs.
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a. Jamal's utility maximizing combination will allocate (spend) his budget and be such that the marginal utility per dollar from the last eclair equals the marginal utility per dollar from the last cream puff. Jamal's utility maximizing combination is 3 eclairs and 2 cream puffs. At this combination, Jamal spends $9 on eclairs (3 eclairs × $3) and $3 on cream puffs (2 cream puffs × $1.50) for a total of $12. The marginal utility from the third eclair is 99 (= 342 - 243), so the marginal utility per dollar from eclairs is 99 ÷ 3 = 33. The marginal utility from the second cream puff is 49.50 (= 103.5 - 54.0), so the marginal utility per dollar from cream puffs is 49.5 ÷ $1.50 = 33. Hence the marginal utilities per dollar are equal, so the combination of 3 eclairs and 2 cream puffs maximizes Jamal's utility.
b. Jamal's new utility maximizing combination is 1 eclair and 4 cream puffs. As in part (a), this combination allocates all of Jamal's income and equalizes the marginal utility per dollar from the two goods. (Both are equal to 21.)
c. When the price of an eclair is $3, Jamal buys 3 eclairs, so one point on Jamal's demand curve is the price of $3 and the quantity demanded of 3 eclairs. When the price of an eclair increases to $6, Jamal buys only 1 eclair. So another point on Jamal's demand curve is the price of $6 and quantity demanded of 1 eclair.
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