Question

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 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) a. b. Assuming the land can fetch a positive rent per unit, how much of it will the worker rent to the c. Given your answer to (b), explain how we can think of the production frontier for the firm as d. What returns to scale does this single input production process have? Draw the production e. What do the worker's indifference curves in this graph look like? Illustrate the worker's f. lustrate the budget for the worker and the isoprofit for the firm that lead both worker and firm g.* In the text, we interpreted this intercept as profit which the worker gets as part of his or her firm in equilibrium (given his or her tastes are only over leisure and consumption)? simply a single-input production process that uses labor to produce output? frontier in a graph with labor on the horizontal and output on the vertical axis. optimal bundle if the worker took the production frontier as his or her constraint. to choose the bundle you identified in (e) as the optimum. What is the slope of this budget/isopfrofit? Does the budget/isopfrofit have a positive vertical intercept? income because the worker owns the firm. Here, however, the worker owns the land that the firm uses. Can you reinterpret this positive intercept in the context of this model (keeping in mind that the true underlying production frontier for the firm has constant returns to scale)? If land had been normalized to 1 unit, where would you find the land rental rate rin your graph?

Answer 1

a)

In such a model where there is only one generic good, assuming the price of output (or one of the three prices) to be equal to 1 simplifies the model. Therefore, wage (w) and rent (r) are then measured relative to the price of output.

b)

The worker will be willing to rent the land till the point where his marginal utility of leisure equals the marginal utility of consumption.