Let a monopolist face a demand function given by P(q) = 40-q and let the cost function be given by C(q) = 50 + q2.
a. Calculate the marginal cost.
b. Calculate marginal revenue.
c. State the condition that a monopolist uses to derive the optimal output.
d. Use the condition from question 11c to calculate the optimal output a monopolist will produce, call that output q*.
e. What price will the monopolist charge, call that price P*?
f. What is the average cost at the quantity of output that the monopolist will optimally produce.
g. Calculate the profit that the monopolist will earn.
h. Calculate the consumers surplus and the producer's surplus.'.
i. calculate the deadweight loss resulting from the existence of monopoly in this market..
j. If the monopolist was practicing a competitive market pricing scheme then calculate the output that he would have produced, call that output qc.
k. Calculate the elasticity of demand that price P=P*.
l. Draw a diagram plotting all the numbers you derived in question 11a-11j and include the relevant cost curves and the demand function.