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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

Expert verified

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

01

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.

02

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.

03

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:

04

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).

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Most popular questions from this chapter

Anne has a job that requires her to travel three out of every four weeks. She has an annual travel budget and can travel either by train or by plane. The airline on which she typically flies has a frequent-traveler program that reduces the cost of her tickets according to the number of miles she has flown in a given year. When she reaches 25,000 miles, the airline will reduce the price of her tickets by 25 percent for the remainder of the year. When she reaches 50,000 miles, the airline will reduce the price by 50 percent for the remainder of the year. Graph Anneโ€™s budget line, with train miles on the vertical axis and plane miles on the horizontal axis.

Suppose that Bridget and Erin spend their incomes on two goods, food (F) and clothing (C). Bridgetโ€™s preferences are represented by the utility function U(F, C) = 10FC, while Erinโ€™s preferences are represented by the utility function U(F,C) = 0.20F2C2.

a. With food on the horizontal axis and clothing on the vertical axis, identify on a graph the set of points that give Bridget the same level of utility as the bundle (10, 5). Do the same for Erin on a separate graph.

b. On the same two graphs, identify the set of bundles that give Bridget and Erin the same level of utility as the bundle (15, 8).

c. Do you think Bridget and Erin have the same preferences or different preferences? Explain.

The price of DVDs (D) is \(20, and the price of CDs (C) is \)10. Philip has a budget of $100 to spend on the two goods. Suppose that he has already bought one DVD and one CD. In addition, there are 3 more DVDs and 5 more CDs that he would really like to buy.

a. Given the above prices and income, draw his budget line on a graph with CDs on the horizontal axis.

b. Considering what he has already purchased and what he still wants to purchase, identify the three different bundles of CDs and DVDs that he could choose. For this part of the question, assume that he cannot purchase fractional units.

If Jane is currently willing to trade 4 movie tickets for 1 basketball ticket, then she must like basketball better than movies. True or false? Explain.

Brenda wants to buy a new car and has a budget of \(25,000. She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from 1 to 10, with 10 representing either the most styling or the best gas mileage. While looking at the list of cars, Brenda observes that on average, as the style index increases by one unit, the price of the car increases by \)5000. She also observes that as the gas-mileage index rises by one unit, the price of the car increases by \(2500.

a. Illustrate the various combinations of style (S) and gas mileage (G) that Brenda could select with her \)25,000 budget. Place gas mileage on the horizontal axis.

b. Suppose Brendaโ€™s preferences are such that she always receives three times as much satisfaction from an extra unit of styling as she does from gas mileage. What type of car will Brenda choose?

c. Suppose that Brendaโ€™s marginal rate of substitution (of the gas mileage for styling) is equal to S/(4G). What value of each index would she like to have in her car?

d. Suppose that Brendaโ€™s marginal rate of substitution (of the gas mileage for styling) is equal to (3S)/G. What value of each index would she like to have in her car?

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