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1) Qopy Qatt specializes in printing business cards and resume is, using the latest laser technology. After analysis of the business, the manager has determined that weekly demand can be approximated by Q=25,000 - 1000P. The firm's cost function is C=25,000 + 13Q + .002Q^2, where Q is output per week.
A) Determine the profit maximizing price and output.
For profit maximization MR = MC
To calculate MR, first write the demand equation in reverse order
P=(25000-Q)/1000 = 25-0.001Q
MR=dTR/dQ = 25-0.002Q
MC=dTC/dQ = 13+0.002*2Q = 13+0.004Q
13+0.004Q = 25-0.002Q
Solving we get Q =12/0.006= 2000
B) The night supervisor believes that extending Qopy Qatt's hours by two 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 Qopy Qatt remain open later in the evening on a permanent basis?
If the current production level is below 2000 units, then it would make sense to keep Qopy Qatt remain open later in the evening on a permanent basis. If the current capacity is more than 2000 units, then it will decrease the profits and would not make sense.
C) A former employee decides to sue Qopy Qatt, alleging employment discrimination. Although management claims innocence, they agree to settle out of court. The settlement requires Qopy Qatt 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.
The weekly payments will increase by $2500, thus the new cost function will become C=27500+13Q+0.002Q^2
Since, there is no change in he variable cost, the optimum price and quantity will remain same as above, but the profits will decrease by $2500 per week.
2) Night Timers is a small company manufacturing glow-in-the-dark products. One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors. Night Timers' chief engineer anticipates that the product will be sold in ten-foot rolls. At present, the company's maximum production capacity is 140,000 rolls per year. The engineer believes the cost function to be described by: C = $50,000 +0.25Q Night Timers' president seeks to establish a price that maximizes profit. She thinks that the firm should be able to sell at least 125,000 rolls of tape per year.
A) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only sell 100,000?
At break even price TC=TR
At 125000 tapes
TC = 50000+0.25*125000=81250
Break even price = 81250/125000=$0.65
At 100000 tapes
TC = 50000+0.25*100000=75000
Break even price = 75000/100000=$0.75
B) The marketing manager forecasts demand for the tape to be: Q = 350,000 - 200,000P. Find the firm's profit-maximizing output and ...
In this case, marginal cost is examined.