Question

**Consider an industry composed by two firms -- Argyle (A)
and Blantyre (B) -- that sell a standardized product. They maximize
their profits by choosing how much to produce. The total output of
this industry (X) is the sum of the output of the two firms
(****X = x _{A}+x_{B} )**

**Both firms have no fixed cost, and a constant
marginal cost equal to c1=10. So the cost function is the same
for the two firms, and equal to c(x)=10x**

**The demand function of consumers is as
follows:**

**X=(210-p)/(2)**

**Where p is the price of the
product.**

(b) What is the profit function for Argyle?

(C) what is the profit function for Blantyre?

(d) -URGENT PLEASE ANSWER - Use the *principle of
profit-maximization* to find the best response function (BRF)
of each firm.

(e) What is the profit-maximizing level of output for firm Argyle?

(f) What is the profit-maximizing level of output for firm Blantyre?

Answer #1

Demand function is X = (210 - p)/2 or 2X = 210 - p. This implies inverse demand function is P = 210 - 2X.

a) Profit function for Argyle = ?A = revenue - cost = price * quantity - cost

= (210 - 2X)xA - 10xA

= (210 - 2xA - 2xB)xA - 10xA

= 210xA - 2xA^2 - 2xBxA - 10xA

= 200xA - 2xA^2 - 2xBxA

c) Since cost function is same, the game is symmetric and so profit function for Blantyre is ?B = 200xB - 2xB^2 - 2xBxA

d) Maximize profits by placing the marginal profit equal to zero for both firms

200 - 4xA - 2xB = 0 200 - 4xB - 2xA = 0

xA = 50 - 0.5xB and xB = 50 - 0.5xA

These are the best response functions

e) Solve the two BRFs

xA = 50 - 0.5*(50 - 0.5xA)

xA = 50 - 25 + 0.25xA

xA = 25/0.75 = 100/3 = 33.33. The profit-maximizing level of output for firm Argyle is 33.33 units

f) The profit-maximizing level of output for Blantyre xB = 50 - 0.5*33.33 = 33.33units.

Consider an industry composed by two firms -- Argyle (A) and
Blantyre (B) -- that sell a standardized product. They maximize
their profits by choosing how much to produce. The total output of
this industry (X) is the sum of the output of the two firms (X =
xA+xB ) Both firms have no fixed cost, and a constant marginal cost
equal to c1=10. So the cost function is the same for the two firms,
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