This question is meant to give you an understanding of what happens when we try to maximize profits with CRS production functions.

A farmer produces riceRusing seedsSand fertilizerF. The production function is given by:

R= min{S,F}

Suppose seeds costpSand fertilizer costspF.

(a) Is the production function homogenous? Is it homothetic?

(b) What is the optimal bundle of seeds and fertilizer needed to produceRunits

of delicious rice. What is the cost function in terms ofR, pSandpF?

(c) Suppose this farmer gets a price ofpfor the rice she sells. Write the expression for farmer's profit, in terms of output price, output level and input prices. What is her

marginal revenue and marginal cost?

(d) Suppose marginal revenue is higher than marginal cost, and she is producing

output levelR1. How much does her profit increase by if she increases production toR2> R1? What does this imply for her optimal choice of output? [Hint:R1was an arbitrary output level.]

(e) Following up on (d), what is her optimal choice of output if marginal revenue

is lower than marginal cost? What if marginal revenue is equal to marginal cost?