=+16.8 Business Application: Valuing Land in Equilibrium: Suppose we consider a Robinson Crusoe economy with one worker who has preferences over leisure and consumption and one firm that uses a constant returns to scale production process with inputs land and labor.

A. Suppose that the worker owns the fixed supply of land that is available for production. Throughout the problem, normalize the price of output to 1.

a. Explain why we can normalize one of the three prices in this economy (where the other two prices are the wage w and the land rental rate r).

b. Assuming the land can fetch a positive rent per unit, how much of it will the worker rent to the firm in equilibrium (given his or her tastes are only over leisure and consumption)?

c. Given your answer to (b), explain how we can think of the production frontier for the firm as simply a single-input production process that uses labor to produce output?