Suppose the firm is hiring labor and capital and that the ratio of marginal products of the two inputs equals the ratio of input prices. Does this imply that the firm is maximizing profits? Why or why not?

Plot an Isocost line for a firm that is spending $10,000 on labor and capital.  Then, draw a Cobb-Douglas Isoquant for this firm that intersects your Isocost curve.  Label the two intersection points A and B.  Draw a second Isosquant that is just tangent to the Isocost curve, and label the point of tangency point C.  Explain why it would not be efficient for this firm to produce at point A nor point B.

3. Elsa's handicrafts has the production function f(x1,x2) = (min{x1 ,2x2})2, where x, is the amount of plastic used, x, is the amount of labor used, and f(x1,x2) is the number of lawn ornaments produced. Let w, be the price per unit of plastic and w, be the wage per unit of labor. а. What is Elsa's cost function c(w1,w2,y)? b. If wi = w2 = 1, then what is Elsa's marginal cost of producing y units of output? What is the number of units of output that she would supply at price p? At these factor prices, what is her average cost per unit of output? c. If the competitive price of the lawn ornaments she sells is p = 48, and w, = w2 = 1, how many will she produce? How much profit will she make? d. More generally, at factor prices w, and w2, what is her marginal cost? At these factor prices and an output price of p, what is the number of units she will choose to supply?

1. The market price for tomatoes is $2/pound. Lynn is too small to influence the price of tomatoes. Her tomato (short-run) production function is given by q= L3 where L measures hours of labor and q measures pounds of tómatoes. (a) demand curve for labor. Lynn hires labor from a competitive labor market. Find her short run (b) elastic than her short-run demand for labor? Explain your answer. Would you expect Lynn's long-run demand for labor to be more or less