Li a very careful maximizer of utility consumes two services

Li, a very careful maximizer of utility, consumes two services, going to the movies and bowling. She has arranged her consumption of the two activities so that the marginal utility of going to a movie is 20 and the marginal utility of going bowling is 10. The price of going to a movie is $10, and the price of going bowling is $5. Show that she is satisfying the requirement for utility maximization. Now show what happens when the price of going bowling rises to $10.

Solution

The utility maximization point is

MUx/Px=MUy/Py, where X is going to watch movie and Y is enjoying bowling

20/10=10/5

2=2, This shows that while consuming the current set of combination of movies and bowling Li is maximizing her satisfaction.

When price of bowling rises to 10

20/10>10/10, this shows that the consumer is not at equilibrium at the current set of consumption.