The following schedule shows demand and total cost for a monopolistic competitor

Question

The following schedule shows demand and total cost for a monopolistic competitor:



Price Quantity Total Cost
30 10 200
29 11 208
28 12 217
27 13 227
26 14 238
25 15 250
24 16 263







a) Calculate what level of output this monopolistic competitor should produce if he/she wishes to maximize profits.



b) At this level of output, what profits will be earned?




c) Calculate the marginal revenue and marginal cost associated with the last unit of output in the table above.



d) If this last unit of output were produced, would it increase or decrease profits?

Explanation / Answer

a) Let P = a - bQ be the demand equation. At P = 30, Q = 10 and at P = 29, Q = 11 so, 30 = a - b*10 and 29 = a - b*11 so, 30-29 = -10b +11b = b => b = 1 and a = 40 HENCE, P = 40 - Q OR P + Q = 40 All other values of P, SATISFY THIS EQUATION. So, R = P*Q = 40Q - Q^2 => MR = dR/dQ = 40 - 2Q Let TC = a + bQ + cQ^2 at Q=10, TC = a+10b+100c= 200 at Q= 11, TC = a +11b +121c = 208 at Q = 12, TC = a+12b +144c = 217 on subtracting first eqn from 2nd one, b+21c = 8 on subtracting first eqn from 3rd one, 2b+44c = 17 on subtracting twice of first eqn from 2nd one immediately above, we get 2c = 1 hence c = 0.5, b = -2.5 and a= 175 so TC = 175 -2.5Q +0.5Q^2 let us check, at Q = 16, TC = 175 - 40 + 128 = 263 , (IT IS OK) So, MC = dTC/dQ = -2.5 + Q For max profit, MR = MC => 40 - 2Q = -2.5 + Q => 3Q = 42.5 => Q = 14.17 (say Q = 14) (ANSWER) b) Profit = R - TC = PQ -TC = (40Q - Q^2) - (175 -2.5Q +0.5Q^2 ) => = 175 + 42.5Q - 1.5Q^2 => max profit = 175 + 42.5*14 - 1.5*14^2 = 476 (at Q = 14) (ANSWER) c) (at Q = 16), MR = 40 - 2Q = 40 -32 = 8 (ANSWER) MC = -2.5 + Q = -2.5 + 16 = 14.5 (ANSWER) d) At Q=16, Profit = 175 + 42.5Q - 1.5Q^2 => = 175 + 42.5*16 - 1.5*16^2 = 471 (NASWER) So it is lower than max profit so, output at Q=16, decreases profit. (ANSWER)

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