Income and substitution effects Consider a consumer that orders her preferences according to the following utility function defined over pizza p and beer b u(b,p) = bp The price of a bottle of beer equals 2 dollars per bottle, and the price of a pizza equals 10 dollars per pizza. Suppose the consumer's income equals 100 dollars. a. Write down the consumer's optimal consumption problem. b. How many pizzas does the consumer buy? How many bottles of beer? c. Let bottles of beer be on the y-axis. Plot your solution and draw the budget line in black ink. Label the optimal bundle with the letter "O." Suppose, now, that the price of beer decreases to 1 dollar per bottle. d. Suppose that the consumer is compensated for the decrease in the price of beer with sufficient money so that she can just barely afford the consumption bundle that she initially purchased before the price decrease. What would her new income be? e. How many bottles of beer and pizzas does the c
2 Income and substitution effects Consider a consumer that orders her preferences according to the following utility function defined over pizza p and beer b u(b,p) = bp The price of a bottle of beer equals 2 dollars per bottle, and the price of a pizza equals 10 dollars per pizza. Suppose the consumer's income equals 100 dollars. a. Write down the consumer's optimal consumption problem. b. How many pizzas does the consumer buy? How many bottles of beer? c. Let bottles of beer be on the y-axis. Plot your solution and draw the budget line in black ink. Label the optimal bundle with the letter "O." Suppose, now, that the price of beer decreases to 1 dollar per bottle. d. Suppose that the consumer is compensated for the decrease in the price of beer with sufficient money so that she can just barely afford the consumption bundle that she initially purchased before the price decrease. What would her new income be? e. How many bottles of beer and pizzas does the consumer purchase at the lower price point of beer and her new income? f. Using red ink, draw the new budget line and label the new optimal point as "C's." g. Does the substitution effect of the decrease in the price of beer lead the consumer to purchase more or fewer bottles of beer? Pizzas? How many more or less of each? h. How many beer bottles and pizzas does the consumer purchase at the new prices and her original income? i. Draw this new budget line in blue ink and label the new optimal consumption bundle as point -F." Your graph should have 3 budget lines and 3 labelled points. j. Draw lines that are perpendicular to the y-axis (beer consumption) and pass through O, Cs, and F. Label the income effect, the substitution effect, and the total effect of the price change on demand for bottles of beer. What is the magnitude of the substitution and income effects? k. Explain the economic importance of decomposing the effect of a price change into the income and substitution effect.
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