Question

Discuss how management utility maximization goal of a firm create principal-agent

problem? How can this problem be solved in an insurance company? A monopolist has a cost

function 200q + 15Q2

and faces a demand function given by P= 1200 – 10Q. Calculate total

revenue, marginal revenue, output and price that maximize profit-maximizing? What is its

maximal profit? Explain with the help of graphs?

Answer 1

The main reasons for the principal-agent problem are conflicts of interests between two parties and the asymmetric information between them (agents tend to possess more information than principals). The principal-agent problem generally results in agency costs.

Total revenue is:

$TR = P×Q = 1200Q - 10Q^2.$

Marginal revenue is:

$MR = TR'(Q) = 1200 - 20Q.$

Output and price that maximize profit exist at MR = MC, so:

$MC = TC'(Q) = 200 + 20Q,$

1200 - 20Q = 200 + 20Q,

40Q = 1000,

Q = 25 units,

P = 1200 - 10×25 = 950.

Its maximal profit is:

$TP = TR - TC = 950×25 - (200×25 + 15×15^2) = 15,375.$