QopyQat specializes in printing business cards and resumes, using the latest las
ID: 1236356 • Letter: Q
Question
QopyQat specializes in printing business cards and resumes, using the latest laser technology. After analysis of the business, the manager has decided that weekly demand can be approximatedby Q = 25,000 - 100*P
The firm's cost function is
C = 25,000 + 13Q + .002 *Q2 ( Q square), where Q is output per week.
a) Determine the firm's optimal output and price
b) The night supervisor believes that keeping QopyQat open longer , for two more hours in the evening would substantially increase volume. The manager is willing to stay open for two hours over the next three months as an experiment. What results would lead you to recommend that the store remain open later in the evening on a permanent basis?
c) A former employee decides to sue QopyQat, alleging employment discrimination. Although management claims innocence, they agree to settle out of court. The settlement requires QopyQat to pay the employee $10,000 per month for the next year. Determine the optimal price and output for the shop under these new conditions.
Explanation / Answer
a) Determine the firm's optimal output and price
Optimal price and output occurs where MC = MR
MC = derivative of the cost function with respect to Q:
C'(Q) = 13 + 0.004Q = MC
Likewise, MR = derivative of the demand function, with respect to Q (note that we must first rearrange the function such that P is on the left-hand side, by itself!)
Q = 25,000 - 100P
P = 250 - 0.01Q
P'(Q) = -0.01 = MR
Now set these equal to each other:
-0.01 = 13 + 0.004Q
-13.01 = 0.004Q
Q = 3252.5
Finally, let's plug Q = 3252.5 back in to our demand equation to solve for the corresponding price, P:
3252.5 = 25,000 - 100P
P = $217.48
b) The night supervisor believes that keeping QopyQat open longer , for two more hours in the evening would substantially increase volume. The manager is willing to stay open for two hours over the next three months as an experiment. What results would lead you to recommend that the store remain open later in the evening on a permanent basis?
If MC = MR is maintained, the firm will continue to maximize its profits and the later opening should be maintained.
c) A former employee decides to sue QopyQat, alleging employment discrimination. Although management claims innocence, they agree to settle out of court. The settlement requires QopyQat to pay the employee $10,000 per month for the next year. Determine the optimal price and output for the shop under these new conditions.
Now we have a fixed cost of $10,000(12) = $120,000
Fortunately, fixed cost does NOT affect marginal cost (or marginal revenue, for that matter!). Since our MC curve will still be above the ATC curve, the firm does not need to shut down, and hence will continue operating at the same Q and P as in (a).
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