Question

The following is a total cost curve. 1000, Total cost ($) 0 50 100 150 200 250 300 350 Quantity (9) On the diagram to the right, sketch the corresponding marginal cost curve. Marginal cost per unit ($) Using the multipoint curved line drawing tool, draw the firm's marginal cost curve. Label this curve 'MC'. Note: Use the multipoint curved line drawing tool one time to draw the entire curve. If the price of output is $3.00 and there are no fixed costs, what is the profit-maximizing level of output? 0.00+ 0 50 100 150 200 Quantity (9) 250 300 350 units of output. (Enter your The firm will maximize profits by producing response as an integer.)

Answer 1

The total cost has constant slopes, meaning that the marginal cost has also constant terms. The marginal cost is
MC=19 0ܠ
. For Q less than or equal to 100, we have
MC=100-0 200-0
or . For Q between 100 and 200, we have
MC = 2 200 - 200 200-100
or . For Q more than or equal to 200, we have
MC =- 600 - 200 300-200
or . The marginal cost can hence be stated as
12 for 0<Q < 100 MC = {0 for 100<Q < 200 14 for 200<Q < 300
.

The marginal cost graph would be as below.

Marginal cost per unit ($) MC 0 50 100 150 200 Quantity (9) 250 300 350

The firm produces where either MC=P or at the highest quantity where MC has not exceeded P. That is where Q=200, which would be the profit maximizing quantity. The graph is as below.

Marginal cost per unit ($) MC P = $ 3 0 50 100 150 200 Quantity (9) 250 300 350

As can be seen, the price P is just below (haven't exceeded) P at Q=200. Hence, the profit maximizing firm will produce 200 units of output.