A Monopolist Faces a Demand Curve Q = 120 -

question 73

Essay

A monopolist faces a demand curve Q = 120 - 2p and has costs given by C(Q)= 20Q + 100.
a.Write the monopolist's profits in terms of the price it charges.
b.Use the derivative (w.r.t.price)to determine the monopolist's profit-maximizing price.
c.Now,derive the monopolist's inverse demand based on the demand equation above.Write out the monopolist's profits in terms of quantity.
d.Use the derivative w.r.t.Q to determine the monopolist's optimal quantity.What price does the monopoly charge?

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Definitions:

Stamens

The male fertilizing organ of a flower, typically consisting of a pollen-containing anther and a filament.

Vegetative Structure

Parts of a plant (such as roots, stems, and leaves) that are involved in growth and development rather than reproduction.

Male Portion

The part of a plant or animal responsible for producing male gametes, such as pollen in plants or sperm in animals.

Flower

Reproductive organ of a flowering plant, consisting of several kinds of modified leaves arranged in concentric rings and attached to a modified stem called the receptacle.