Question

The average cost of living is approximately the same in the following four​ cities: Sarasota,​ FL; Cleveland,​ OH; Cheyenne,​ WY; and​ Phoenix, AZ. Use the information you have learned about marginal utility and the substitution effect to explain whether you believe a​ consumer's purchasing choices would remain the same in each of these cities. Assume that her income would be the same in each city.

Answer 1

In this problem, there are four cities. Average costs of living of these cities are same. Also, incomes in each city are same. You have to answer whether composition of different goods purchased will remain the same or not. Answer will depend upon availability of substitutes.

Objective of a consumer is to maximize his satisfaction. It is ascertained by comparing marginal utility (MU) with price. Here satisfaction from last unit of the commodity is MU. Suppose it is $10. Compare it with price. If $6 is paid for buying, then consumer is getting $4 extra satisfaction. It is known as consumer's surplus. So long this consumer surplus from marginal unit is positive he will buy it. Thus equilibrium will be attained where MU and price are equal.

Now assume that person has two commodities to consume. They are substitutable. Here ideal combination of two commodities will depend upon the MU per dollar. Divide MU by the price to get it. Suppose MU per dollar of first commodity is 8 and for 2nd commodity is 5. As first one is giving higher MU per dollar, consumer will better off by taking more units of commodity 1 and less units of commodity 2. Due to increase in quantity of 1 consumed, MU will decrease. It will happen since law of diminishing utility is operative.

As per this law, if you go on consuming the quantity of a specific commodity, keeping the consumption of others constant, then MU of it will gradually decrease. Just opposite will happen for commodity 2. Here it will increase. Ultimately optimum combination will be selected when MU per dollar of two commodities are equal. Thus utility is optimized when:

`(MU_(1))/(P_(1)) = (MU_(2))/(P_(2))`

However, selection of this optimum combination will depend upon the availability of two commodities. Suppose, in one town commodity 1 and commodity are adequately available. But in another town, availability of commodity 1 is restricted. In that situation, consumer will not be able to take best bundle of choice. He will be forced to take more 2 and less of commodity 1. Limited availability of substitution has forced him to consume differently, obviously his satisfaction will be low.

Thus, cost of living of four cities Sarasota,​ FL; Cleveland,​ OH; Cheyenne,​ WY; and​ Phoenix, AZ may be equal. Also income of four cities are same. Yet choice of commodities will differ. It is due to the adequacy of availability of substitutes.