The market for internet services is perfectly competitive. Joe’s Internet Servic
ID: 1209601 • Letter: T
Question
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.
Explanation / Answer
a) For profit maximixation MC=P=MR as price is revenue firm for sale of additional unit.
12q+5=53
q=48/12=4
TC=6*16+5*4+20= 136
Revenue= 53*4=212
Profit = 212-136=$76
b) Now TC = 6q^2+7q+20 MC = 12q+7
MC=p so 12q+7=53 so q = 46/12 = 3.83
The points of intersection of price and MC curves is the profit maximization points
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