DEMAND FUNCTION 
 
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 COST 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. 
TOTAL PROFIT:  Subtracting total cost from total revenue gives profit. It is the distance between the red and blue lines. At Q_{o} = 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 The corresponding price is


AVERAGE and MARGINAL COST  
Average cost AC = TC / Q Marginal cost MC = DTC / DQ

PRICE and MARGINAL REVENUE  
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 Q_{o }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. 



