Here are the steps to solve this problem: 1) Take the derivative of total cost (TC') = 400 - 40Q + 3Q^2 2) Set TC' equal to marginal revenue (MR) and solve for Q: TC' = MR 400 - 40Q + 3Q^2 = 309.75 - Q 3Q^2 - 39Q + 91.25 = 0 3) Solve the quadratic formula to find the optimal quantity: Q* = 13 4) Plug Q* back into the demand equation to find price: P* = 309.75 - 13 = 296.75 5) Calculate total cost at Q* and subtract from total revenue to find profit:

1. MONOPOLISTIC
COMPETITION
Perfect competition , where all goods are
homogenous and all firms are price takers , is
rarely seen. Imperfect competition is very
common . In this kind of a market , there are few
sellers and product differentiation and price wars

2. Differences between
monopolistic and perfect
competition.
While firms in a monopolistic markets are
price dictators , in perfect competition they are
price takers.
The demand curve for a market based on
perfect competition is a horizontal straight
line, while in imperfect competition the
demand curve slopes downwards from left to
right

3. Differences between monopolistic and perfect
competition.
In perfect competition there is constant returns to
scale, while imperfect competition is based on
the the principal of increasing returns to scale.
Under perfect competition increase in output is
equal to increase in input. But under imperfect
competition , an increase in input leads to more
than proportionate increase in output.This allows
some firms to occupy a dominant position in the
industry. These firms set the price for the entire
industry

4. Characteristis of mperfect
competition
An imperfect market can be defined as a market
with many producers offering goods which are
close substitutes, but not identicals as is the case
in the perfect competition. Since the products
vary in their features , the pricing also varies.

5. Under imperfect competition sellers try to
differentiate their products mainly on the basis of
four aspects
• Physical features
• Location
• Services
• Product image

6. Market structure characteristics
of monopolistic competition
• Number and size distribution of sellers
• Number and size distribution of buyers
• Product differentiation
• Conditions of entry and exit
• Many small sellers. Actions of
individual sellers go unheeded by
other firms
• Many small buyers
• Slightly differentiated. Product of
one firm is a close substitute for
that of other sellers
• Easy entry and exit

7. Profit –maximizing price and
output in the short run
price
p
MC AC
D
MR
Qc

8. Long run profit maximization in
the monopolistic competition
mc ac
Pc

9. The manager of a firm has the
following demand equation given by
P=309.75-Q and the long run cost
equation is TC=400Q-
20Q2
+Q3
Where Qis quantity. What is
the long run equilibrium price and
quantity how much economic profit
will the firm earn?

10. The manager of a firm has the
following demand equation given by
P=309.75-Q and the long run cost
equation is TC=400Q-
20Q2
+Q3
Where Qis quantity. What is
the long run equilibrium price and
quantity how much economic profit
will the firm earn?