Mark likes to eat pizzas and watch TV. In order to buy pizzas, he is looking for a job that pays him a wage of $w per hour for L hours of labor. Since he can only work a maximum of 15 hours a day (Mark needs 9 hours of sleep to function) and he cannot watch TV while working, he needs to decide how to allocate his time between working and watching TV during the time when he is awake, which is always a tough decision. Specifically, Mark's utility from pizzas and TV is:

U(P,T)=2ln(P)+ln(T)

where P is the number of pizzas and T is the number of hours he spends on TV. (Assume both P and T are infinitely divisible.)

1. Suppose a pizza costs 10 dollars. What will be Mark's daily budget constraint over pizzas and TV as a function of P, T, and w?

2. What are the magnitudes of the Marginal Rate of Substitution (MRS) and Marginal Rate of Transformation (MRT) of television for pizzas as functions of P, T, and w?

Mark finds a job that pays him $2/hour. How many hours will he spend on watching TV in a day and how many pizzas will he eat?

P=

T=

4. Suppose that Mark is eligible for $5 of food stamps per day. Now how many hours will he spend on watching television, and how many pizzas will he eat?

P=

T=

5. Illustrate the budget constraints, indifference curves, and optimal consumption levels found in (3) and (4) in the same graph with television on the horizontal axis.