Case 1
Consider a monopolistic firm facing the following demand and total cost functions
If the firms wants to sell the whole output Q it cannot charge more than P(Q) per unit. Its total revenue will be
TR(Q) = P(Q).Q
It will cost the firm TC(Q) to produce output Q. What remains after subtracting total cost from total revenue is the profit of the firm
PR(Q) = TR(Q)  TC(Q)
In the next table total revenue and profit are calculated
We can see that the maximum profit 70 is obtained at optimal output Q_{o }= 15 and monopoly price P_{m} = 8. Total revenue is 8 times 15, that is 120 and total cost is 50.
Click on the GRAPH button to see the graph of total revenue, total cost and profit.
Finally we know that maximum profit is obtained when marginal cost equals marginal revenue
MC = MR
This table demonstrates that at Q = 15 and P = 8 both marginal cost and revenue equal 4. Avrerage cost is 3.3 so that total cost is 3.3 times 15 that is 50.
Push the GRAPH button to see the graph of marginal and average variables.



