Question

please answer all of the following questions since theyre all related

(1)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?

Answer 1

Sop @ price (o)= 460 total cost (TC) = 28 + 69Q - 14Q+Q Total Revenue (Te) = D.CO. [TR= 6087 The equilibrium price and output determine by the order conditon (Foc) of profit maxínu zorion. profit first (FCC) of • profit function TR TR - TC To Goga - 128 - 699 + 1402 - 3 . a = 1402-08 - 9Q. - 128 • foc sfer profit maximization requires com = 0] da = 280 - 30²-gco. do 30-280 +9=0 90* -Q-276 +90 (30-4) - 9 (30 - 1) =0 (3Q-1 (0-9)=0 30-1 to or 0-9 20 To = 1/3 or Q = 9) second order condition for profit maxi macation requires [ da co] El d (280-30²-9) . da da 01 = 28 - 60 put value of a = 1/3 or a = 9 it Q= 1/3 ,then a 2 = 28-6(13)

28-2 do² da = 26 do2 = 26 70 not satisfied the second order condition, in this case gecond order condition satisfied the profit minimisation Condo. if Q= 9, then de 28-(9) dhm = 28-54 doz - - 26 o 2025 second order satisfied the Condition. Result :- profit maximisation ouiput 9=97 TR= 60(R) to ©. Marginal reventie (mr) = ? MR CTR on from a do (from eq@ o MR = d Goa da. IMRE 607 [MR = 607 : Marginal Cost ( oc) = ? me do me= dtc 1. Imc = d 128 + 69 Q - 140 + Q de 69 - 280 + 30

geaphical representation :- MR= 60 mc= 69 – 28Q + 30€ li213 The 4151617189110 MC 4425 12 124 165 541920 37 6087 MC: 64- 280 302 mRipoti mciso - MR = 60 - - - ories 4 5 6 7 8 9 10 11 12 is a output in perfect competition profit maximise at where MC CURVE intersect mr curve le IMC = MR in this case profit maximisation output at point E , where a = ]. ☺ ... in pesefect competition profit maxinvigation Cound - MC = MR 69-28Q + 30% - 60 3QP-280 +950 Solve this quaedratic equation, we get 3Q-1) = 0 or (Q-9)=0 [Q=/ or Q291 Q=9)

equilibrium price and output P=60 , Q = 9 = 140² - 8² - 98 - 1287 profit function, put value of "Q=9" we get maximum profit T= 14 ()- (9)*- 9 (9) - 128 (n = 196) Result:-at Q=9, maximum prefit of firm 1=196!