DEMAND FUNCTION
 Q is quantity P(Q) is price

Suppose a monopolistic firm is facing the   demand  function shown on the left. P(Q) is the price at which the consumers are willing to buy the quantity Q,  therefore, the firm cannot charge more than P(Q)  if  it wants to sell the whole output Q .

 TOTAL REVENUE TR(Q) = P(Q).Q Total Revenue of the firm (TR) from selling the whole output Q can be obtained simply by multipying price and quantity.

 TOTAL COSTIt will cost the firm TC(Q) to produce output Q. Note that Total Cost function is given by the technology available to the firm and by  prices of factors (labor, capital, etc.) and other inputs.

 TOTAL PROFIT: PR(Q) = TR(Q) - TC(Q) Subtracting total cost from total revenue gives profit.  It is the distance between the red and blue lines.At Qo = 5 the total revenue is 15, total cost is 10, and profit is 5.
 TOTAL PROFIT: PR(Q) = TR(Q) - TC(Q) Maximum profit  is obtained at  Qo = 5.The  corresponding price  is  P = 3 (see the demand function). This is the monopoly price.

 AVERAGE and MARGINAL COST Average costAC = TC / QMarginal costMC =  DTC / DQ

 PRICE and MARGINAL REVENUE Marginal revenueMR =  DTR / DQThe black curve is the demand function which is price P plotted against quantity Q. Marginal revenue lays always bellow the demand function.

 SOLUTION OF THE MONOPOLY PROBLEM Optimal quantity of output Qo that maximizes monopoly profit is determined by the intersection of the blue and red curves, that is by   MC = MR  In our case :Qo=5 ,  P=3, MC=MR=1.5,  AC=2,  TC=10, TR=15 and monopoly profit is    PROF=5. Note that if this firm were not monopoly but a firm under perfect competition, than the optimal solution would be where   P = MC, or at the intersection of the red and black curves. At that point quantity of output would be approximately  9, so that the following would hold:  Q=9, P=MC=2.24, AC=1.95, TC=17.55, TR=20.16, and profit would be PROF=2.61.

 OK Economics was designed and it is maintained by Oldrich Kyn. To send me a message, please use one of the following addresses: okyn@bu.edu --- okyn@verizon.net This website contains the following sections: General  Economics: Economic Systems: Money and Banking: Past students: http://econc10.bu.edu/okyn/OKpers/okyn_pub_frame.htm Czech Republic Kyn’s Publications American education