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Chapter 3: Problem 15

Connie has a monthly income of \(\$ 200\) that she allocates between two goods: meat and potatoes. a. Suppose meat costs \(\$ 4\) per pound and potatoes \(\$ 2\) per pound. Draw her budget constraint. b. Suppose also that her utility function is given by the equation \(U(M, P)=2 M+P .\) What combination of meat and potatoes should she buy to maximize her utility? (Hint: Meat and potatoes are perfect substitutes.) c. Connie's supermarket has a special promotion. If she buys 20 pounds of potatoes (at \(\$ 2\) per pound), she gets the next 10 pounds for free. This offer applies only to the first 20 pounds she buys. All potatoes in excess of the first 20 pounds (excluding bonus potatoes are still \(\$ 2\) per pound. Draw her budget constraint. d. An outbreak of potato rot raises the price of potatoes to \(\$ 4\) per pound. The supermarket ends its promotion. What does her budget constraint look like now? What combination of meat and potatoes maximizes her utility?

Short Answer

Expert verified
Under the new pricing scheme where the price of potatoes increases to $4 per pound, Connie's utility maximizing combination is to buy meat only.

Step by step solution

01

Determining Budget Constraints

To determine the budget constraints, we need to understand the trade-off between the two goods (meat and potatoes), given their prices and Connie's income. With an income of $200, at a price of \( $4 \) per pound of meat and \( $2 \) per pound of potatoes, the maximum amount of meat she can buy is 50 pounds (\( $200 / $4 \)) and 100 pounds of potatoes (\( $200 / $2 \)). The budget constraint equation is \( 4M + 2P \leq 200 \) where \( M \) is meat and \( P \) is potatoes.
02

Maximizing Utility

The utility function given is \( U(M, P) = 2M + P \). As meat and potatoes are perfect substitutes, she would choose the good with a higher per dollar utility. Therefore, we should calculate the utility/dollar for both meat and potatoes. For meat, \( Utility/dollar = 2/4 = 0.5 \), and for potatoes, \( Utility/dollar = 1/2 = 0.5 \). Given equal utility, she could spend her entire budget on either good. However, her choice should be an affordable combination of meat and potatoes.
03

Incorporating Promotional Offers

The supermarket promotion alters Connie's budget constraint. The first 20 pounds of potatoes cost her \( $40 (20*$2) \), with an additional 10 pounds free. Therefore, she could spend the remaining \( $160 \) on meat and additional potatoes. Hence, additional potatoes will increase the budget limit beyond the initial straight line.
04

Revised Budget Constraint after Price Change

An increase in the price of potatoes to \( $4 \) modifies the budget constraint and the utility per dollar. The new utility per dollar for potatoes is \( Utility/dollar = 1/4 = 0.25 \), which is less than the utility per dollar for meat (0.5). Hence, Connie should spend her entire income on meat.

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