5. A monopoly firm maximizes profit by producing at the point where MR = MC.
For this firm, TR= 4Q
Therefore, MR = d(TR)/dQ = 4
And, TC = 0.04Q3 - 0.9Q2 + 10Q + 5
Therefore, MC = d(TC)/dQ = 0.12Q2 - 1.8Q+ 10
Setting MR = MC, we get
0.12Q2 - 1.8Q + 10 = 4
Or, 0.12Q2 - 1.8Q + 6 = 0
Multiplying both sides by 0.12 we get,
Q² - 15Q + 50 = 0
Or, Q² -(10+5)Q + 50 = 0
Or, Q² - 10Q - 5Q +50 = 0
Or, Q(Q - 10) -5(Q - 10) = 0
Or, Q = 10 ; Q = 5
Therefore, the firm will be maximizing profit by producing either 10 units or 5 units. So, the best level of output it will be producing is 10 units as it is greater than 5 units.
b) When Q = 10, TR = (4*10) = 40 and TC = 0.04(10)³ - 0.9(10)² +(10*10) + 5 = 40 - 90 + 100 + 5 = 55
Therefore, total profit at this best level of output is (TR - TC) = (40 - 55) = -15, that is a loss of $15.
3.5 5. A firm's total-revenue and total-cost functions are TR 40 TC 0.0403-0.90+ 100 +5 (a)...
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1. A firm has the following demand and total cost schedule. TR Profit MR MC O 0 10 20 30 40 50 60 P 100 90 80 70 60 50 40 TC 200 400 600 800 800 1,000 1.200 1.400 a) Is the firm a price-taker or price searcher? Explain. b) Complete the Total Revenue (TR) and Profit schedules. c) How many units of output (Q) should the firm produce to maximize profits? d) What price (P) should the...
Consider a competitive firm with total costs given by TC(q) = 100 + 10q + q 2 The firm faces a market price p = 50. (a) Write expressions for total revenue TR and marginal revenue MR as functions of output q. (b) Write expressions for average total cost ATC, average variable cost AVC, and marginal cost MC as functions of output q. (c) For what value of output is ATC minimized?
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