Exam 7: Costs

A firm has a production function given by . Suppose that each unit of capital costs R and each unit of labor costs W. a. Derive the long-run demands for capital and labor. b. Derive the total cost curve. c. Derive the long-run average and marginal cost curves. d. How do marginal and average costs change with increases in output? Explain.

Use the following table to answer the question. At an output of 4, the average fixed cost is $____.

A firm's production function is given by Q = KL, where MP_L = K and MP_K = L. The wage rate (W) = $50, and the rental per unit of capital (R) is $12.50. In the short run, capital (K) is fixed at 10 units. The short-run average total cost of producing 100 units of output is _____, and the long-run average total cost of producing 100 units of output is _____.

Suppose a firm's total cost curve is TC = 5Q² + 6Q + 125. The firm's marginal cost is MC = ____.

Use the following table to answer the question. At an output level of 2, the variable cost is $____.

Sanjay's hair salon has a total cost function given by . Sanjay's average variable cost is AVC = ____.

Given the cost function TC = 200 + 4Q + 2Q², the average cost equation is_____. This means that the average variable cost portion is _____ and average fixed costs portion is _____.

Lilly's Lumberyard had the following revenues and costs last year: If Lilly did not own a lumberyard, she would earn $115,000 per year as a store manager for Home Depot. Lilly's Lumberyard had an economic cost of _____ and an economic profit of _____.

Suppose a firm's total cost curve is TC = 5Q² + 6Q + 125. The firm's average variable cost is AVC = ____.

Which of the following statements is (are) TRUE? I. If marginal cost is rising, the average total cost must be rising. II. The marginal cost curve intersects both the average total and average variable cost curves at their minimum points. III. If marginal cost is less than average variable cost, the average variable cost curve is negatively sloped.

(Figure: Supply and Quantity I) Refer to the graph. Do you agree or disagree with the following statement? Why? "If the firm can sell its product for $30 and it's selling 12 units, it should close its doors and produce nothing, since it is losing money."

A firm with a production function Q = KL (where K is units of capital and L is units of labor) has an expansion path that is given by K = 2L. The wage rate (W) is $20 and the rental on capital is $10. Assuming that the firm is using the optimal mix of inputs for any given output level, the total cost when using one unit of labor is $____.

A firm has a production function of Q = KL + L, where MP_L = K + 1 and MP_K = L. The Wage rate (W) is $100 per worker and the rental (R) is $100 per unit of capital. In the short run, capital (K) is fixed at 4 and the firm produces 100 units of output. The firm's short-run total cost of producing 100 units of output is $____.

Determine whether each of the following statements is TRUE or FALSE. a. The slope of the total cost curve is equal to marginal cost, or the change in variable cost divided by the change in output. b. AFC = ATC - AVC c. The average total cost cannot equal marginal cost. d. Total cost can increase as a result of an increase in variable cost.

If TC = 1,500 + 7.5Q + Q², the cost function for ATC is ATC = ____.

(Figure: Cost and Quantity of Output II) The total cost of producing an output of 24 is $____.

A fixed cost:

Anvi runs a coffee shop that has annual revenues of $300,000, supply costs of $60,000, and employee salaries of $60,000. She has the option of renting out the coffee shop for $80,000 per year, and she has three outside offers from competitors to work as a senior barista at Starbucks (for an annual salary of $30,000), at Simon's coffee house (for an annual salary of $40,000), and at Peet's coffee shop (for an annual salary of $60,000). She can only hold one job at a time. What should Anvi do?

Sanjay's hair salon has a total cost function given by . . Sanjay's average total cost is ATC = ____.

Menard quit his high school teaching job, which paid $60,000 per year, to start a business that prepares students for the SAT exam. His first year in business generated the following revenues and costs: Menard's economic profit is $____.