Question

Assume quantities need not be integers. A monopolist incurs marginal cost equal to MC=Q per unit and faces demand P(Q)=10 - 2 x Q. If there is no fixed cost for production, what is the total cost of production?

Answer 1

The total cost of production for a monopolist with the marginal cost MC=Q and no fixed costs is determined by integrating the marginal cost function, resulting in the total cost function TC=(1/2)Q^2.

Step-by-step explanation:

To determine the total cost of production for a monopolist with a marginal cost (MC) function equal to MC=Q per unit, one would integrate the marginal cost function with respect to quantity (Q). In calculus, the total cost (TC) function is the integral of the marginal cost function when the variable cost is the only type of cost, which is the case here since there is no fixed cost for production.

The integral of MC=Q with respect to Q is (1/2)Q^2. Therefore, the total cost function is TC=(1/2)Q^2. This represents the area under the marginal cost curve from 0 to Q.

Note that this model assumes that quantities need not be integers and that the marginal cost function starts from zero, meaning the monopolist does not have any fixed costs.