table of demand function DEMAND FUNCTION
Q is quantity P(Q) is price

 

monop_demfu1.gif (3175 bytes)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

 

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.

 

 

 

 

 

mon_tab_TC1.gif (2899 bytes)

 

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:
 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.

 

mon_tab_PR1.gif (4717 bytes)

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.

 

mon_tab_PR1.gif (4717 bytes)monop_profit1.gif (3696 bytes)

 

 

 

 

 

AVERAGE and MARGINAL COST

Average cost

AC = TC / Q

Marginal cost

MC =  DTC / DQ

 

 

 

 

 

 

PRICE and MARGINAL REVENUE
mon_tab_MR1.gif (3832 bytes)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

monop_marginal1.gif (5947 bytes)

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 :
Q
o=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.

 

 

 

 

 

 

 

 

 

 

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