Question

The production function for a firm in the business of calculator assembly is given by ? = 2√?. Where q denotes finished calculator output and l denotes hours of labor input. The firm is a price taker both for its output (which sells at P) and for workers (which can be hired at a wage rate of w per hour).

(a) What is the total cost function for this firm? [Hint: write total cost function as a function of output q and input price w.]

(b) What is the supply function for assembled calculators when the firm maximizes its profit? [The supply function is essentially the optimal output as a function of all prices].

(c) Using the results in (a) and (b), obtain the firm’s profit function. [Hint: Write the profit function as a function of P and w].

(i) How does an increase in output price affect the profit of the firm? Explain

  (ii) Is the profit function homogeneous of degree 0, 1, or 2? Explain

(d) What is the firm’s input demand function for labor? [Hint: write the input demand function as a function of P and w].

(i) How does an increase in the wage rate affect the demand for labor? Explain.

(ii) Is the input demand function homogeneous of degree 0, 1, or 2? Explain.

Answer 1