Question

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) = 2M + 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

a. Connie's budget constraint when meat costs $4 per pound and potatoes $2 per pound:

b. Connie can choose any combination between (100,0) to (0,200) on the price line, which will maximize her utility.

c. Connie's budget constraint after special promotion:

d. Connie's budget constraint after special promotion ends:

Connie will maximize her utility when her consumption bundle for meat and potatoes are (30,20).

Step-by-step solution

Connie's budget constraint

Connie's budget equation is:

4M + 2P = 200

The budget constraint is shown in the figure below:

The intercept of x-axis is 200/2=100, and the intercept of y-axis is 200/4=50.

Various combinations of meat and potatoes

Given that the meat and potatoes are perfect substitutes,the price line or budget line corresponds to the indifference curve when goods are perfect substitutes (complete substitution allows zero consumption of one good).

For the utility function:

U(M, P) = 2M + P

the budget equation is 4M + 2P = 200

Subject to the budget constraint, the combination of meat and potatoes are:

(4 x 50) + 0 = 200

(4 x 30) + (2 x 40) = 200

(4 x 10) + (2 x 80) = 200

(4 x 0) + (2 x 100) = 200

Thus, Connie can choose any combination between (50,0) to (0,100) on the price line, which will maximize her utility.

Budget line after supermarket's special promotions

Connie's budget equation is:

4M + 2P = 200

For P = 20

4M + 2(20) = 200

4M + 40 = 200

4M = 200 - 40

M = 40

Connie gets extra 10 potatoes on a purchase of 20 pounds at $2 per pound. Connie's actual consumption bundle becomes (30,40) due to the supermarket's special promotion.

The new budget line will be:

Budget line after supermarket's special promotion ends

Connie's budget equation when the price of potato is $4:

4M + 4P = 200

Since, supermarket ends promotion, at P=20, the amount of meat purchased will be:

4M + 4(20) = 200

4M + 80 = 200

4M = 200 - 80

M = 30

The budget line will be:

Hence, Connie will maximize her utility when her consumption bundle for meat and potatoes are (30,20).