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 $wper hour forL 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 pn TV.

What are the magnitudes of the Marginal Rate of Substitution (MRS) and Marginal Rate of Transformation (MRT) of television for pizzas as functions ofP,T, andw? (Hint: the inverse MRS and MRT are not provided as answers.)

MRS_PT=

a. 2

b. none of these options

c 2/P OVER 1/T

d. 2ln (P)/ln(T)

e. 1/2

MRT_PT=

a. 10w

b. none of these options

c. the MRT cannot be determined from the provided information

d. 15w

e. 10/w