Three firms have identical revenue and profit functions. Firm 1 is a private sec
ID: 1107542 • Letter: T
Question
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)= 140q-2q^2
And a cost function of
C(q) = 20+40q
Determine how much output each firm chooses
Firm 1 will produce such that : Q= ____ Units ?( Enter response as a whole number for all 3)
Firm 2 will produce such that: Q = _____ Units ?
Firm 3 will produce such that: Q = ____ Units ?
Explanation / Answer
We have the following information
Revenue function = R(q) = 140q – 2q2
Cost function = C(q) = 20 + 40q
Firm 1: (Maximizing profit)
Profit (P) = Revenue – Cost
P = 140q – 2q2 – 20 – 40q
P = 100q – 2q2 – 20
P/q = 100 – 4q = 0
For maxima the second derivative should be negative
2P/P2 = – 4
So, 100 – 4q = 0
4q = 100
Profit maximizing output (Q) = 25
Firm 2: (Revenue maximization)
R(q) = 140q – 2q2
R(q)/q = 140 – 4q = 0
For maxima the second derivative should be negative
2R(q)/P2 = – 4
So, 140 – 4q = 0
4q = 140
Revenue maximizing output (Q) = 35
Firm 3: (Employment maximization subject to revenue being non-negative)
R(q) = 140q – 2q2
Equating revenue function equal to Zero to get the output level at which the revenue is positive
R(q) = 140q – 2q2 = 0
q(140 – 2q) = 0
140 – 2q = 0
2q = 140
Employment maximizing output (Q) = 70