13) Pierre, a Frenchman with a weakness for champagne, recently received a raise

Question

13) Pierre, a Frenchman with a weakness for champagne, recently received a raise. His income rose from $25,000 to $40,000 a year. As a result, Pierre's consumption of Andre Champagne decreased from 15 bottles a week to 5 bottles a week. Calculate Pierre's income elasticity of demand for Andre Champagne. What might be the reason for the decrease in demand?

14) Your friend the grocer lowered the price of chicken from $2.50/pound. to $1.75/pound. He was dismayed to see that the quantity demanded of hamburger decreased from 80 pounds to 64 pounds per week. Since you are the neighborhood economist, he comes to you for an explanation. Respond by calculating cross elasticity of demand. Then explain what happened to the grocer’s sales.

Explanation / Answer

(13)

Change in quantity demanded = (5 - 15) / 15 = - 0.67

Change in income = (40,000 - 25,000) / 25,000 = 0.60

Income elasticity of demand = Change in quantity demanded / Change in income

= - 0.67 / 0.6 = - 1.12

Since income elasticity is negative, it is an inferior good. A plausible explanation is, with increased income, Pierre will reduce consumption of Andre Champagne and will buy more of some other (possibly more expensive) brand of wine.

(14)

Change in price of chicken = $(1.75 - 2.50) / $2.50 = - 0.3

Change in quantity demanded of hamburger = (64 - 80) / 80 = 0.2

Cross-price elasticity of demand = Change in quantity demanded of hamburger / Change in price of chicken

= - 0.3 / 0.2 = - 1.5

Since cross-price elasticity is negative, this indicates that chicken and hamburger are complements.

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