Managerial Econ510, Problem Set 3: Chapter 6. Prob. 10, Chapter 7 prob. 8

Jul 14th, 2016
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10. A firm uses a single plant with costs C  160  16Q  .1Q2 and faces the price equation P  96  .4Q. a. Find the firm’s profit-maximizing price and quantity. What is its profit? b. The firm’s production manager claims that the firm’s average cost of production is minimized at an output of 40 units. 8. Firm Z, operating in a perfectly competitive market, can sell as much or as little as it wants of a good at a price of $16 per unit. Its cost function is C  50  4Q  2Q2. The associated marginal cost is MC  4  4Q and the point of minimum average cost is Qmin  5.

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Problem Set 3: Managerial EconomicsKalicharan PachikaMay 30, 2016Chapter 7:Q no. 8A.MR =$16 and MC= MR= 4+4Q =164Q=12Q=3So, the profit maximizing level of output is 3 unitsTR = PQ = 16 x 3 = 48and TC = 50+4Q + 2QTC = 50+4(3) + 2(3) = 80as profit is TR - TC = 48-80=-32B.Q=200 - 5p=200 - 516Q=200-80 =120The number of supplying firms in the market is: 120 3= 40C.In the long run, there are some firms who will not be able to survive and they will exit themarket and the price will increase and output will decrease. This will occur when the pricesreach a minimum level of AC=24, LR equilibrium demand=175. So the number firms that willstill operate 35=1755.D.As this industry is in perfect competition, so in the short run the firms are earning highprofits but in the long run when new firms will enter into the market, then the prices willdecrease because of the increased output and competition level. P = MC = MR = AR = ACChapter 6:Q no. 10a)It is given that total cost functionC=160+16Q+0.1Q (2)And Equation of price:P= 96-0.4Q.Total Revenue (TR) function:R=PQ=96Q-0.4Q (2).While total profit function:F=R-C= (96Q-0.4Q (2))-(160+16Q+0.1Q (2))

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