# profit-maximizing equilibrium

A market's total demand is given by P = 80-(z/2). This market is supplied by a "dominant firm" and by other, relatively "small firms". The small firms' total supply is given by P=4y. The dominant firm's total cost function is TC = (x^2)/20 + (17x/9) + 10, marginal cost function is MC = (x/10) + 17/9, marginal revenue curve is MR = (640-8x)/9

(a) Find the equation of the dominant firm's derived-demand function(p as a function of x)

(b) find the equation of the dominant firm's total revenue(TR)

(c) calculate the dominant firm's output X and price P at its profit-maximizing equilibrium.

Â© BrainMass Inc. brainmass.com December 15, 2022, 7:03 pm ad1c9bdddfhttps://brainmass.com/economics/general-equilibrium/profit-maximizing-equilibrium-demand-function-192828

#### Solution Preview

A market's total demand is given by P = 80-(z/2). This market is supplied by a "dominant firm" and by other, relatively "small firms". The small firms' total supply is given by P=4y. The dominant firm's total cost function is TC ...

#### Solution Summary

This posting finds profit-maximizing equilibrium.