Marginal cost and average variable cost

Question

Question: If the marginal cost of producing a good is increasing as a firm produces more of the good and then which of the following must be true?

a) AFC is rising 
b) AVC is rising 
c) MC > AVC  
d) MPL is falling

Question: The equality of marginal cost and average variable cost occurs when:

a) Marginal cost is minimal.     
b) Average product of the variable input is minimal. 
c) Average variable cost is minimal.  
d) None of the previous statements is correct.

Question: Suppose the short-run production function is Q = 10L and the wage rate equals $10.  Find the average variable cost.

Question: A firm’s total cost function is given by TC = 2Q² + 10. What are the firm’s fixed costs, variable cost, average fixed cost, average variable cost, and marginal cost functions?  Sketch the MC, AFC, AVC curves, as well as the average total cost curve, all in one diagram. If necessary, continue your solution on the back side.

Question: A firm uses capital and labor to produce a single output good. The production function is given by F(K, L) = K² L; Where K is the amount of capital and L is the amount of labor employed by the firm.  The unit prices of capital and labor are, respectively, r = $6 and w =$5.  Let the amount of capital K be fixed at K=20. Based on this information, determine and sketch the firm’s short run cost curves: AFC, AVC, AC, and MC. Please use the back of this page if you need more space for your solution.

Question: A firm uses capital and labor to produce a single output well. The production function is given by F(K, L) = K² L; Where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, respectively, r = $6 and w =$5. Based on this information, please draw the optimal expansion path of the firm. Explain.

Question: Let a firm’s production function be given by K^0.3 L^0.7.

(i) Sketch (without specific numbers) the shape of the long run average and long-run marginal cost curves of the firm;

(ii) in the same graph, please also sketch the firm’s short run average and marginal cost curves (when the amount of capital is fixed). Comment on the relationship between the long- and the short-run curves.

Question: A firm operates two plants with the marginal cost curves given by MC₁ = 50 + 2Q₁, MC₂ = 90 + Q₂. If the firm’s total output must be 80 units, how much will it produce at each plant?  Please use the back of this page for your solution.

Question: Let a quarry’s cost function of producing Q tons of stone per hour be given by TC =  Q³- 10Q²+ 40Q + 25, so that marginal cost function is MC= 3Q² - 20Q + 40.

(i) Find the formula for the quarry’s short-run supply curve and draw its detailed graph. Explain your solution.

(ii) If market price of a ton of stone is $28, how much will the quarry’s manager be willing to produce per hour in the short run? Calculate per hour profit.