Here is two example questions: rest can be found in the file attached.
2. We are first in a pure and perfect competition framework. A firm X produces a
quantity QX of plastic bags made using oil, which the firm sells to supermarkets at
the equilibrium price p
∗ = 80. The total cost of production function can be written
this way:
CT (QX) = 2Q
2
X + 20QX + 200
a. Find the fixed cost, the variable cost and the marginal cost of production function of the firm X.
b. Write down the optimality condition of the production of a firm in perfect
competition. Determine the number of plastic bags produced at the optimum.
c. Calculate the profit of the firm at the optimum and determine if the profit is
positive or negative. What would be the fixed cost that would make the profit
equal to zero?
4. Following a new environmental regulation, the distribution of plastic bags made using
oil is forbidden in all supermarkets. Among the numerous firms of the sector, only
firm X has sufficiently well anticipated the regulation change and has the technology
2
necessary for the production of biodegradable bags using corn. The firm manages
to eliminate all its competitors and ends up in a monopoly situation on this market.
It keeps the same cost function than in question 2.
a. What are the two hypothesis of pure and perfect competition that are not valid
anymore in this framework?
b. The aggregated demand for the production of plastic bags is D(p) = 200 − 2p.
Calculate the inverse demand function p(QX) and explain why it decreases with
production.
c. Write down the equation of the profit of the monopoly. Knowing that the
marginal revenue is Rm = 100 − QX, deduce from it the optimal production
and the monopoly price.
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