Question:

The Paradise Shoes Company has estimated its weekly TVC function from data collected over the past several months, as TVC = 3450 + 20Q + 0.008Q2 where TVC represents the total variable cost and Q represents pairs of shoes produced per week. And its demand equation is Q = 4100 – 25P. The company is currently producing 1,000 pairs of shoes weekly and is considering expanding its output to 1,200 pairs of shoes weekly. To do this, it will have to lease another shoe-making machine ($2,000 per week fixed payment until the lease period ends).

1. Describe and derive an expression for the marginal cost (MC) curve.
2. Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).
3. What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.
4. Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications which underlie your recommendation.

(Please show all your calculations and process. Describe your answer for each question in complete sentences, whenever it is necessary.)

(b) The incremental costs of 200 shoes is 20 + 0016*200 = 23.2

We need to add 2000 to this so total is equal to 2023.2.

(c) Equate MC with MR:

P = (4100-Q)/25

TR = Q*(4100-Q)/25

MR = (4100-2Q)/25 = 820-.08Q

MC = 20 + .016Q

20 +.016Q = 820 -.08Q

800 = 0.096Q

so then Q = 800/0.096 = 8333.33.

(d) We need to distinguish between short and long run. In the short run profits are maximized at Q = 8333.33. An expansion to 1200 will not maximizes profits.

However in the long run, if the firm thinks that demand is likely to go up then it could consider expansion and the new lease required. The cost of taking a new lease of 2000 is justified only when we expect demand to rise.

Economics in the Current News

Take some time to think about the ways in which your learning in this class relates to the real world. Has the knowledge you gained been valuable in helping you understand or evaluate events or policies? Are there any current events in the news that you can directly link to concepts or theories covered so far?

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