The market for internet services is perfectly competitive. Joe's Internet Services has total cost function TC(q) = 6q2 + 5q + 20 and marginal cost function MC(q) = 12q + 5.
(a) The current price per unit of internet services is $53. Determine the output level that maximizes Joe's profit in the short run. Determine the resulting profit for Joe's.
(b) The coefficient on the q term in the total cost function depends on a robotics input price. Suppose this input price increases to 7.
Draw a single graph depicting the market price (still $53), the initial MC curve (before the increase in the input price) and Joe's initial profit-maximizing choice; and the new MC curve (after the increase in the input price) and Joe's new profit-maximizing choice. Be sure to explicitly show the coordinates for intercepts and for any other important points in the graph.