Ar 60 2 q g mr 6 06 q h mr 10 i tr 60 q 3 q 2 j tr 60

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= AR = 60 – 2 Q (g) MR = 6 – 0.6 Q (h) MR = 10 (i) TR = 60 Q – 3 Q 2 (j) TR = 60 Q 2. Maximum Total Revenue is reached when MR = 0. For cases (a) to (j) in Exercise 1, find Q* , the value for Q that maximizes Total Revenue, and give the value of Total Revenue at that point. 3. The Total Cost function this period for a firm producing Electric Cheese (“the cheese with shockingly good taste!”) is given by the equation TC = 16 + 4 Q + Q 2 , where TC is in $ and Q is in kilograms. (a) Give the following functions for Electric Cheese: Fixed Cost (FC), Variable Cost (VC), ATC, AFC, AVC, and MC. [If you do not have calculus, and even if you do, you may want to check page 349, n. 14 of the text.] (b) By using calculus or by using the rule that MC = ATC at the minimum point of ATC, calculate the level of Q at which ATC is at its minimum. (c) If Electric Cheese sells at the jolting price of $24/kg, and profits are maximized when P = MR = MC, calculate the profit-maximizing level of Q , Q* , and the level of profits (= TR – TC) this period, when the firm produces at this level of output. 4. A company’s Total Revenue function this period is given by the equation TR = 60 Q – 0.5 Q 2 and its Average Total Cost function is given by the equation ATC = 10/ Q + 15 + Q , where TR is in $, Q is in units, and ATC is in $/unit. (a) Profit-maximization occurs where MC = MR. Give the equations for the MC and MR curves and calculate Q *, the profit-maximizing level of Q . (b) Calculate the company’s profits this period at Q *. 5. A company’s Average Factor Cost of Labour (or labour supply) function this period is given by the equation AFC L = 20 + L and its Marginal Product of Labour function is given by the equation MP L = 40 – L ,
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where AFC L is in $/labour-day, MP L is in kg/labour-day, and L is in labour-days. It can sell as much output as it wants at a constant price of $3/kg. It has no fixed costs. (a) Profit-maximization occurs where MFC L = MRP L . Give the equations for the MFC L and MRP L curves and calculate the profit-maximizing level of L , L *. (b) Calculate the company’s profits this period at L *. M5-6 MATH MODULE 5: TOTAL, AVERAGE, AND MARGINAL FUNCTIONS
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