|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 .|
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.
It 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.
|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.
PR(Q) = TR(Q) - TC(Q)
Maximum profit is obtained at
The corresponding price is
AVERAGE and MARGINAL COST
AC = TC / Q
MC = DTC / DQ
|PRICE and MARGINAL REVENUE|
MR = DTR / DQ
The 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 :
|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.