# Microeconomics - Profit maximization, elasticity, marginal

The Alvin Corporation is the only producer of a particular type of laser. The demand curve for its product is:

Qd = 8,300 -2.1P

And its total cost function is:

TC = 2,200 + 480Q +20Q²

Where P is price (in dollars), TC is total cost (in dollars), and Q is monthly output

a. To maximize profit, how many lasers should the firm produce and sell per month?

b. If this number were produced and sold, what would be the firm's monthly profit?

c. Is demand elastic, inelastic or unit elastic at the profit maximizing price - quantity

combination?

d. What is the excess of price over the marginal cost at the profit maximizing price-

quantity combination?

https://brainmass.com/economics/elasticity/profit-maximization-elasticity-marginal-cost-example-problem-235113

#### Solution Preview

(a) Profit, PR = Revenue - Cost = QP - TC = [Q(8300 - Q)/2.1] - (2200 + 480Q + 20Q^2)

= 3952.38Q - 0.4762Q^2 - 2200 - 480Q - 20Q^2 = -20.4762Q^2 + 3472.38Q - ...

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided.