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Three firms have identical revenue and profit functions. Firm 1 is a private sector firm operated...

Three firms have identical revenue and profit functions. Firm 1 is a private sector firm operated by an​ owner-manager who wishes to maximize profit. Firm 2 is managed by an​ revenue-maximizing manager whose pay is proportional to the​ firm's revenue. Firm 3 is a​ government-owned firm that has been instructed to maximize the amount of​ employment, L, subject to the constraint that revenue must not be negative.

Each of the three firms has a revenue function R(q)=140−2q^2 and a cost function of ​C(q)=80+40q.

Determine how much output each firm chooses.Firm 1 will produce such that q= _____ units. 

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given that:

Three firms have identical revenue and profit functions. Firm 1 is a private sector firm operated by an​ owner-manager who wishes to maximize profit. Firm 2 is managed by an​ revenue-maximizing manager whose pay is proportional to the​ firm's revenue.

Firm 1:

MR(Marginal revenve) = MC(Marginal cost)

TR = 140q - 2q2

MR = 140 - 4q

TC = 80 + 40q

MC = 40

The profit maximizing condition is

MR = MC

140 - 4q = 40

4q = 100

q = 100 / 4 = 25 units

FIrm 1 will produce such that q = 25 units

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