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Julio receives utility from consuming food (F) and clothing (C) as given by the utility function U(F,C) = FC. In addition, the price of food is \(2 per unit, the price of clothing is \)10 per unit, and Julio's weekly income is $50.

a. What is Julio's marginal rate of substitution of food for clothing when utility is maximized? Explain.

b. Suppose instead that Julio is consuming a bundle with more food and less clothing than his utility-maximizing bundle. Would his marginal rate of substitution of food for clothing be greater than or less than your answer in part a? Explain.

Short Answer

Expert verified

a. Julio's marginal rate of substitution of food for clothing when his utility is maximized to 31.25 is 0.2.

b. Julio's marginal rate of food substitution for clothing does not change as the prices are the same, although he consumes a bundle with more food and less cloth.

Step by step solution

01

Marginal rate of substitution at the utility-maximizing condition

For the given utility function, Julio will maximize his utility when:

MUCPP=MUFPFF10=C2F=5C

The consumption bundle can be computed from the budget line as:

2F + 10C = 50

(2x5C)+10C=50

C=2.5

then F=12.5

Putting the relation in the utility function:

U(C,F)=FC=12.5×2.5=31.25

The marginal rate of substitution is:

MRSF,C=MUFMUC=PFPC=CF=PFPC=2.512.5=15

Julio's marginal rate of substitution is 0.2.

02

For the change in consumption bundle

The marginal rate of substitution of two goods is the ratio of the prices of the goods.

The utility-maximizing consumption bundle is (12.5, 2.5). If the consumption for food increases from 12.5 and consumption for cloth decreases from 2.5, the marginal substitution rate remains the same.

The MRS does not change because prices of per unit food and cloth remain the same after the consumption bundle changes.

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Most popular questions from this chapter

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.

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a. Illustrate Ben’s optimal bundle on a graph with pizza on the horizontal axis.

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c. Suppose instead that pizza is rationed at a quantity less than Ben’s desired quantity. Illustrate Ben’s new optimal bundle.

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Suppose that Jones and Smith have each decided to allocate $1000 per year to an entertainment budget in the form of hockey games or rock concerts. They both like hockey games and rock concerts and will choose to consume positive quantities of both goods. However, they differ substantially in their preferences for these two forms of entertainment. Jones prefers hockey games to rock concerts, while Smith prefers rock concerts to hockey games.

a. Draw a set of indifference curves for Jones and a second set for Smith.

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