Drew chooses how much to work each day on a farm that he owns. He

enjoys both leisure (i.e. time not spent on working) and the food that

he gets from the farm.

(a) Suppose that if Drew works for fraction x of his waking hours, he

produces food for consumption c according to the function:

c =

p

x x:

Draw the feasible set of possible choices of leisure l = 1 x and

c for 0 x 1. What is Drew's marginal rate of transformation

(MRT)? Is Drew's marginal product of work diminishing? Is it

always positive?

(b) Draw indierence curves between leisure and food consumption

for Drew under the assumption that he needs more food to give

up a unit of leisure at lower levels of leisure. Find the optimal

amount of food and leisure graphically.

(c) Suppose next that Drew nds a new type of seed that improves the

food production to c = 2

p

x x. Discuss the eects of the new

production technology on Alex' optimal consumption of leisure.

Can you say for sure if his optimal working hours increase or

decrease as a result of the new seed?