3. Assume that producers want to maximize prots and that they are in a perfectly competitive market. Revenue that producers earn is given by: ptyt, where pt is the price of their output and yr is the quantity of their output. Firms use labor (1,) and capital (kt) to produce output, 31, = f (It, kt). f (It, kt) is the production function and is characterized by diminishing marginal products and constant returns to scale. Firms rent labor (at the nominal wage rate, wt) and rent capital (at the rental rate, 1}") from households. a. (5 points) Given the assumptions described above, describe, both verbally and with an equation, the condition that describes the producers' optimal choice of labor and capital. b. (5 points) Suppose that there is an increase in productivity that increases the marginal products of labor. What happens to the demand for labor? Explain