Question

Jessica derives utility from her consumption of two goods, video game plays on an X-Box (call it good X) and high energy yogurt (call it good Y). Her utility function is U(X,Y) = XY. The price per play of games is $2.00 and the price of yogurt is $10 per container and Jessica's income is $50 per week. She is presently consuming a bundle of game plays and yogurt such that her marginal rate of substitution is 1 (or -1, if you wish). Use this information to answer the following questions.

(4)a. Is Jessica currently consuming the bundle of game plays and yogurts such that her utility is maximized? Explain.

(4)b. If she isn’t choosing her utility maximizing bundle, what adjustment should she make to her consumption bundle?

Answer 1

(A) For consumer equilibrium, the following condition has to be satisfied:

MRS = Px/Py

Formula for MRS = MUx/MUy

Here, MRS is 1 (Given)

Price ratio = 2/10 = 1/5

Hence, here:

MRS > Price Ratio

Clearly, Jessica is not consuming the bundle which maximizes the utility. The logic has already been given above: The condition MRS = Px/Py has to be statisifed

(B) Since, MRS > Price Ratio It means that to obtain one more unit of gameplays,the she is willing to sacrifice more units of Yoghurt  than the market requires. The consumer values more than what market values, that is, she is willing to pay a price higher than the market price. THUS, She should increase consumption of gameplays till MRS declines enough to become equal to the price ratio (when equilibrium is restored). Here the concept of diminishing marginal utility is in play too. It says that an additional unit of consumption comes with a lower marginal utility.