Roman loves corn bread. He buys corn meal and wheat flour in order to make corn bread. His recipe calls for two cups of corn meal and one cup of flour for each batch that he bakes. More corn bread is better for Roman. He can bake fractions of a batch, but has no use for corn meal or flour that is left over. What of the following is Roman’s utility function on cups of corn meal, denoted by c, and cups of flour, denoted by f?

(A) U(c, f)=min{c,2f}
(B) U(c, f)=min{2c, f}
(C) U(c, f)=min{2c,3f}
(D) U(c, f)=min{3c, sf}
(D) U(c, f)=2c+3f

(B) U(c,f)=min{2c,f}

Explanation:

This is an example of Leontif utility function which states that the preferences of a consumer is to a constant ratio of quantities of two or more goods in his demand bundles and having an extra unit of a single good will not increase the utility of the consumer and will make the extra unit to waste. But having more units of all the goods in the demand bundle which maintain the constant ratio will increase the utility of the consumer.

A good example usually used in economics is that of a pair of shoe. Having one right and one left of a type of shoe gives a consumer utility at a constant ratio of 1:1, and increasing each leg by multiple of one at every point in time will increase the utility of the consumer, while increasing just only one makes the utility not to change. For instance, having only two left shoe will not give the consumer any utility and make both the left shoe useless.

In the question, the ratio of cups of corn meal, denoted by c, and cups of flour, denoted by f, is 2:1. This implies that to increase the utility of the consumer, c has to increase by a multiple of 2 at every point in time while f has to increase by one at the same point in time to maintain the constant ratio of 2:1. Increasing only c by 2 or only f by 1 will maintain the constant ratio and it will lead to a waste of the increased unit of the affected commodity.

Therefore, option (B) U(c,f)=min{2c,f} is the correct answer that gives a constant ratio of 2:1 = 2c:f.

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