The Deering Manufacturing Companys shortrun average cost fun

The Deering Manufacturing Company\'s short-run average cost function in 2012 was AC = 3 + 4Q where AC is the firm\'s average cost (in dollars per pound of the product), and Q is its output rate. a. Obtain an equation for the firm\'s short-run total cost function. b. Does the firm have any fixed costs? Explain. c. If the price of the Deering Manufacturing Company\'s product (per pound) is $3, is the firm making profit or loss? Explain. d. Derive an equation for the firm\'s marginal cost function.

Solution

a) The Total cost function is equal to Average cost times the output.

So Deering Manufacturing Company\'s short-run Total cost function is

Total Cost = Average Cost * Quantity

                 = (3+4Q)Q

                 = 3Q + 4Q²

b) The Deering Manufacturing Company does not have any fixed cost because when quantity is zero, the total cost is zero.

c) If the price of the Deering Manufacturing Company product is $3 then the total revenue is 3Q.

Profit = Total Revenue - Total Cost

         = 3Q - (3Q+4Q²)

         = 3Q - 3Q - 4Q²

          = - 4Q²

If Quantity is greater than zero, profit will be negative, and this means that the Deering Manufacturing Company is incurring losses. If the Deering Manufacturing Company is producing nothing, it is incurring neither profits nor losses. Thus, the Deering Manufacturing Company is better off producing nothing.

d) Marginal cost is the derivative of Total cost with respect to Quantity.

Marginal cost = dTC/dQ = 3+8Q