Question

A firm in a perfectly competitive market sells all its product (Q) at a constant price (P) of $60. Suppose the total cost function (TC) for this firm is described by the following equation: 2 3 TC(Q) = 128 + 69Q - 140 + Q (a)Form the profit function and determine the output that maximizes the firm's profit. Evaluate the second order condition to assure that profit is maximized at this level of output. (b)Derive the marginal revenue (MR) and the marginal cost(MC). Graph both curves for Q = 1,2........12 Use the graph to find the level of output that maximizes the firm's profit. (c)Solve algebraically for the profit maximizing output using the MR and MC derived in part (b). (d) How much profit/loss does the firm earn by producing the profit maximizing output? (2)The following equations describe the market for commodity X. Q(p) = 10 + 3P ........................(1) Q(p) = 15 - 2P ................ .....(2)

the firm faces a constant price (P) of $60

Answer 1

Figure 1

80 МС Е MR 40 20 Quantity 10 4 2 6 CO CO -N+ MR!MC

Ca) Profit = 60 Q- 128 - 698 414Q-os FOC = 6o- G9+ 28 Q- 3Q :o 28 Q - -a 9 2 a- 6+ 3Q2.0 3a)-a-36)-o (9-)1-36)o SoC 28 6 : 28 - 6 (9)= -28< o Then profit , mazi miged at MR Curve MR= 60 O Mc = 69 - 28 Q +3 MC urure equilibriwm E Figure C MR = MC equiibrium: AH 6-28 a + 3 Q - a- 28a + 3Q3 3 2 -a + 9 = 0 is maxinmi ged at Profit 6Oxa128- 69(9)t 14 (a)-(a*