question_answer

A consumer consumes only two goods X and Y and is in equilibrium. Show that when the price of good X rises, the consumer buys less of good X. Use utility analysis.

Or

Given the price of a good, how will a consumer decide as to how much quantity of that good to buy? Use utility analysis.

Answer:

In case of two commodities, the consumer?s equilibrium is attained at that point, where; the utility derived from each additional unit of the rupee spent on each of the goods is equal. That is, Marginal Utility of a Rupee spent on the good X (i.e., \[M{{U}_{x}}/P{{ & }_{x}}\]) is equal to the Marginal Utility of a Rupee spent on the good Y (i.e.,\[M{{U}_{y}}/P{{ & }_{y}}\]), which in turn is equal to the Marginal Utility of Money (\[M{{U}_{M}}\])? That is

\[M{{U}_{x}}/P{{ & }_{x}}=M{{U}_{y}}/P{{ & }_{y}}=M{{U}_{M}}\]

However, when the price of commodity X rises, the ratio of marginal utility to price of \[X(M{{U}_{x}}/P{{ & }_{x}})\] becomes lower than that of Y, that is \[M{{U}_{x}}/P{{ & }_{x}}<M{{U}_{y}}/P{{ & }_{y}}\].

In such a case, the consumer rearranges his consumption combination such that the equality is again restored. He would decrease his consumption of commodity X. With the decrease in the consumption of commodity X, marginal utility of X rises. As a result, the ratio of marginal utility to price of X rises. The consumer would continue decreasing the consumption of commodity X till the equality between the ratio of marginal utility to price in case of X and Y is again reached.

Or

In order to decide, how much of a good to buy at a given price, a consumer compares Marginal Utility (MU) of the good with its price (P). The consumer will be at equilibrium, when the Marginal Utility of the good will be equal to the price of the good. i.e., \[M{{U}_{x}}={{P}_{x}}.\] If \[M{{U}_{x}}>{{P}_{x}}.\] that is, when price is lesser than the Marginal Utility, then the consumer will buy more of that good. On the other hand, if \[M{{U}_{x}}<{{P}_{x'}}\] that is when price is more than the Marginal Utility, then the consumer will buy less of good. This is reflected in the following diagram.

In the figure, the quantity of commodity x is represented on the x-axis, while, the price and the utility are represented on the y-axis. OP is the price of the commodity.\[M{{U}_{x}}\]curve is downward sloping representing diminishing Marginal Utility of x. The consumer attains consumers equilibrium at point E, where, the Marginal Utility becomes equal to the price of the commodity.