Econ 2000 - Problem Set 6 (soln)

Econ 2000 Problem Set 6 2. Leaf’s Ribs Company’s short-run cost curve is: C ( q, K ) = 25 q 2 K + 15 K where q is the number of Leaf’s Ribs produced and K is the number of robot chef hours Leaf’s Ribs Company hires. Currently, Leaf’s Ribs Company hires 10 robot chef hours per period. The short-run marginal cost curve is: MC ( q, K ) = 50 q K If Leaf’s Ribs Company receives $250 for every Leaf’s Ribs he produces, what is his profit maximizing output level? Calculate Leaf’s Ribs Company’s profits. Econ 2000 Problem Set 6 3 / 10

Econ 2000 Problem Set 6 Solution: (a) Market supply is the horizontal sum of individual firm supply (firm’s MC curve). Firm’s TC = 90 , 000 + 0 . 00001 Q 2 and MC = 0 . 00002 Q = P. Solve for Q in terms of P to express as supply curve P = 0 . 00002 Q → Q = 50 , 000 P Market supply curve is the horizontal sum of firm supply curve or N-times the firm supply curve (N is the number of firms). N here is equal to 500 QS = 500(50 , 000) P = 25 , 000 , 000 P Equate QS and QD to determine price and quantity. 25 , 000 , 000 P = 90 , 000 , 000 − 20 , 000 , 000 P → 45 , 000 , 000 P = 90 , 000 , 000 P = $2 . 00 Q = 25 , 000 , 000 P = 25 , 000 , 000(2) = 50 , 000 , 000 (b) To determine the firm’s output, equate price and marginal cost - Firm’s MC = 0 . 00002 Q . P = 2 = 0 . 00002 Q → Q = 100 , 000 Firm’s profit π = TR − TC π = 2 . 00(100 , 000) + 0 . 00001(100 , 000) 2 π = 200 , 000 + 190000 = 10 , 000 Econ 2000 Problem Set 6 6 / 10

Econ 2000 Problem Set 6 Solution: (a) Given the competitive nature of the market, Bud should equate P to MC. 2 . 50 = 0 . 001 Q → Q = 2500 TR = 2 . 5 × 2500 = 6250 TC = 2000 + 0 . 0005 = 2000 + 3125 = 5125 π = TR − TC = 6250 − 5125 = 1 , 125 Since the cost function is an economic cost function, we can conclude that this is an economic profit. (b) Tax shifts total cost curve to: TC = 2000 + 0 . 0005 Q 2 + 0 . 5 Q MC becomes MC = 0 . 001 Q + 0 . 5 setting P = MC 2 . 50 = 0 . 001 Q + 0 . 5 2 . 00 = 0 . 001 Q → Q = 2000 TR = 2 . 50 × 2000 = 5000 TC = 2000 + 0 . 0005 + 0 . 5(2000) = 2000 + 2000 + 1000 = 5000 π = 5000 − 5000 = 0 Given that this is zero economic profit, Bud should continue operating. The impact on Bud’s competitors will be favourable or neutral. As he curtails output, 500 Econ 2000 Problem Set 6 9 / 10