Question

(a) Suppose the total revenue (TR) and total cost (TC) curves of
the perfectly competitive firm are given by the following set of
equations: TR = 100Q and TC = Q^{2} + 4Q + 5, where Q is
the output. Derive the firm’s profit maximizing output and
calculate the total and average profit earned by the firm at this
level of output.

(b) How do you know that the equations above could not be referring to a monopoly?

Answer #1

b) Since only Total revenue and Total cost is given and we are to find the profit maximising oitput. And we know that MR=MC ( Mrginal Revenue = Marginal Cost. )

Second question is answered first because it is important for the first question.

a)

Total Revenue is 100Q

So marginal revenue is 100.

Marginal cost is equal to marginal revenue is the profit maximisation condition for Monopoly .

So total revenue is =$4800 (Putting the value of Q in TR)

Total cost is= $ 2501(Putting the value of Q in TC)

Total profit = $2299 (Total Revenue - Total cost )

Average profit is = $47.89 (Total profit /Q)

Please leave a feedback if possible. Thank you!!

1. Suppose a perfectly competitive firm has a cost function
described by TC = 200Q + Q^2 + 225 Each firm’s marginal revenue is
$240. a. Find the profit maximizing level of output. b. Is this a
short-run or long-run situation? How do you know? c. Assuming that
this firm’s total cost curve is the same as all other producers,
find the long-run price for this good.

Monopoly problem: Find TR (total revenue), TC (total cost), P
(price), Q (quantity), Profit & elasticity
Given: TC=10,000+100Q+0.20Q^2
Qd (demand)=20,000-10P

Monopoly problem: Find TR (total revenue), TC (total cost), P
(price), Q (quantity), Profit & elasticity
Given: TC=10,000+100Q+0.20Q^2
Qd (demand)=20,000-10P

Suppose that each firm in a competitive industry has the
following cost curves: Total cost: TC = 32 + 1⁄2 Q2; where Q is the
individual firm’s quantity produced. MC=Q. Assume the market price
is $14 per unit. If the market price falls, how much will each firm
produce in the long run? a. 32 b. 8 c. 11 d. 64

How the Total Revenue curve for a perfectly competitive firm is
different from the Total Revenue curve for a monopoly? Use the TR
curve for a monopoly to explain why the quantity which maximizes TR
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TR = 22Q-0.5Q2
TC = 1/3 Q3 - 8.5Q2 + 50Q+90
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AR > 350/q + 15 + 5q
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