Question

Consider a firm with total costs represented by TC=16+Q^2 and a corresponding marginal cost of 2Q (MC=2Q)

1. Graph the ATC and MC, be certain to label the lowest point of the ATC.

Consider that firm faces a price of 12$.

2. Find the optimal quantity.

3. Graph and find the total cost, total revenue, and any profit or loss at the optimal quantity.

Answer 1

1).

Consider the given problem here the cost function is given by, “C=16+q^2”, => ATC = 116/q + q” and the marginal cost function is given by, “MC=2*q”. Consider the following fig shows the “ATC” and “MC”.

So, here the ATC is “U-shaped” curve and the “MC” is the ray through the origin. So, here “A” be the point where “ATC” is minimum.

2).

Now, if “P=12”, => at the optimum “P=MC”, => 2q=12, => q=12/2=6, => q = 6 units. So, here the profit maximizing output is “q=6 units”. So, at the optimum output the profit is given by.

=> Profit = TR-TC = P*q - (16+q^2) = 12*6 – (16+6^2) = 72-52 = 20 > 0.

3).

Consider the following fig shows the “TR”, “TC” and “profit function”.

So, here the firm is making positive profit of “20”.