Question

1. (60 points) Company X is in a perfectly competitive industry and is in long run. That is, X has not picked its scale and fixed equipment yet. X has two scale options: Option I: TFC $7,500,000, TVC(a) 100+ 10,000 Q2, in $. Option Il: TFC $6,000,000, TVC(Q) 120+ 25,000 Q2, in $. a) (10 points) Plot ATC and MC for both options on the same graph with x-axis representing the quantity and y-axis representing MC and ATC. (You can use any software) b) (10 points) Denote the quantity at which ATC, and ATCi are equal to each other, Qx. Solve Q c) (15 points) What is the minimum price, denoted by Py, at which you would prefer scale I rather than scale lII? d) (15 points) ls P, equal to ATG (ОЈ ? Why or why not? Note that atd., ATO, (Ox) ATCI Ox

Answer 1

Figure 1

a) The graph depicting ATC and MC is given below Figure 1 b) The ATC for both option at Q_x is ATC_1 = TC_1/Q_x = 7500000/Q_x + 10 + 10000 Q_x ATC_11 = TC_11/Q_x = 6000000/Q_x + 12 + 25000 Q_x Now: at Q_x ATC_1 = ATC_11 therefore 7500000/Q_x + 10 + 10000 Q_x = 6000000/Q_x + 12 + 25000 Q_x or, 1500000/Q_x - 2 - 15000 Q_x = 0 or, 1500000 - 2Q_x - 15000 Q^2_x = 0 or therefore Q_x = 9.99 tildeequal 10 c) At Q_x: E_r ATC_1 = ATC_11 = 850010 At the min ATC_1: MC_1 = ATC_1 or, 7500000/Q + 10 + 10000 Q = 10 + 20000 Q or, 750/Q = Q therefore Q^2 = 750: Q = 27.4 p_min = 548010 At the min ATC_11: MC_11 = ATC_11 or, 6000000/Q = 25000 Q implies therefore Q^2 = 240 therefore Q = 15.5 therefore p_min = 775012 Then the minimum price for which the firm will choose scale 1 is P_y = 548010. d) Py does

Then the minimum price for which the firm will choose scale 1 is Py=548010.

d) Py does not equal to ATC1(Qx) because, at Qx, ATC1=ATC2, the firm will be indifferent between two option. To choose one scale the minimum point of the ATC curve should be judged. This is the point that the perfectly competitive firm sustains in the long run. Then if the firm chooses scale 1 for any price less than 775012, the firm will face loss and will be forced out of the market.