Firm K is a leading maker of light-weight, water proof outerwear. During the win

Question

Firm K is a leading maker of light-weight, water proof outerwear. During the winter months, demand for its main line of water proof coats is given by P=800-.2Q where P denotes price in dollars and Q is quantity of units sold per month. The firm produces coats in a single plant (which it leases by the year.) The total monthly cost of producing these coats is estimated to be C=150,000+400Q. Leasing the plant accounts for almost al of the $150,000 fixed cost. If the firms other outerwear products generate $50,000 in contribution, what is the firm's total monthly profit?

B. From time to time corporate customers place special orders for customized versions of Firm K's coat. Corporate orders generate an avg. contribution of $100 per coat. Firm K has just recieved and unexpected order for up to 300 coats but has unused capacity to produce only 200. One manager recomends delivering 200 coats. A second argues for cutting back production of standard coats by 100 to fill the complete order. Who is right? Explain

Explanation / Answer

a) To maximize profit set MR = MC. Therefore, we have MR = 800 - .4Q = 400, implying Q* = 1,000, and P = 800 (.2)(1000) = $600 per coat. The firm's total monthly profit is: (600 400)(1000) + 50,000 150,000 = $100,000. b) If the firm delivers 200 coats, its incremental contribution is ($100)(200) = $20,000, so that its total profit is $120,000. If it delivers 300 coats, its contribution is $30,000 from corporate coats. It now sells only 900 mainline coats (at a price of $620 each). Its contribution from this line is: (620 400)(900) = $198,000. Thus, its total profit is 198,000 + 30,000 + 50,000 150,000 = $128,000. This is the more profitable alternative. Another way of arriving at the same answer is to treat the $100 contribution as an opportunity cost, and add it to the MC of 400. Setting MR = 800 - .4Q = 500, implies Q* = 750. (The firm should be willing to cut back its mainline coat output by 250 coats if needed.) However, it only needs to cut back 100 coats (to fill the corporate order), so Q* = 900 is optimal. Finally, the most direct way to free up winter capacity (as opposed to paying to expand it) is to produce extra coats during the slack summer

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