Suppose a firm A produces a product q, but also pollution x that affects a second firm B. Firm A is a competitive firm and faces an equilibrium price of £12 for its product. The cost function of firm A is . Firm B is a competitive firm and faces an equilibrium price of £10. Firm B’s cost function is .A. Compute the equilibrium prices and quantities and the profits of the two separate, competitive firms. Interpret the first order conditions. Explain. b) Compute the social optimum, that is, the equilibrium prices, quantities, and profit when firm A and B are merged. Interpret the conditions and compare it to the solution in (a). Explain.c) Devise a quantity tax on product q for firm A in (a) such that the government can restore the social optimum in (b). a) Suppose a firm A produces a product q, but also pollution x that affects a second firm B.Firm A is a competitive firm and faces an equilibrium price of £12 for its product. The costfunction of firm A is С₁(q, x) = q² + (x − 4)². Firm B is a competitive firm and faces anequilibrium price of £10. Firm B's cost function is CÂ(r,x) = r² + xr. Compute the equilibriumprices and quantities and the profits of the two separate, competitive firms. Interpret the firstorder conditions. Explain.Ib) Compute the social optimum, that is, the equilibrium prices, quantities, and profit when firmA and B are merged. Interpret the conditions and compare it to the solution in (a). Explain.c) Devise a quantity tax on product q for firm A in (a) such that the government can restorethe social optimum in (b).

The cost function of firm A: Ca(q,x) = q2 + x-42 P=12 The cost function of firm B: Cb (r,x) = r2 +…

Answered: Compute the equilibrium prices and…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose a firm A produces a product q, but also pollution x that affects a second firm B. Firm A is a competitive firm and faces an equilibrium price of £12 for its product. The cost function of firm A is . Firm B is a competitive firm and faces an equilibrium price of £10. Firm B’s cost function is .

A. Compute the equilibrium prices and quantities and the profits of the two separate, competitive firms. Interpret the first order conditions. Explain.

b) Compute the social optimum, that is, the equilibrium prices, quantities, and profit when firm A and B are merged. Interpret the conditions and compare it to the solution in (a). Explain.

c) Devise a quantity tax on product q for firm A in (a) such that the government can restore the social optimum in (b).

a) Suppose a firm A produces a product q, but also pollution x that affects a second firm B.
Firm A is a competitive firm and faces an equilibrium price of £12 for its product. The cost
function of firm A is С₁(q, x) = q² + (x − 4)². Firm B is a competitive firm and faces an
equilibrium price of £10. Firm B's cost function is CÂ(r,x) = r² + xr. Compute the equilibrium
prices and quantities and the profits of the two separate, competitive firms. Interpret the first
order conditions. Explain.
I
b) Compute the social optimum, that is, the equilibrium prices, quantities, and profit when firm
A and B are merged. Interpret the conditions and compare it to the solution in (a). Explain.
c) Devise a quantity tax on product q for firm A in (a) such that the government can restore
the social optimum in (b).

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