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 = 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, 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.

Now imagine that Argyle and Blantyre merge into one single firm. The firm that results from the merger of these two giants is called Cargiltyre. As a result of the merger, there is now only one firm in the industry: Cargiltyre. The demand function of consumer remains the same as before.

(j) How much output will Cargiltyre produce?

(k) What price will Cargiltyre charge for its product?

(l) How much profits will Cargiltyre make?

Answer 1

Cargiltyre becomes a monoply and so it produces monopoly output. Cost structure is same so both divide the total production equally wuth combined MC = 10. Inverse demand is P = 210 - 2X. This gives the profit function for Cargiltyre as

? = TR - TC

= 210X - 2X^2 - 10X

Maximize profits by placing marginal profit = 0

210 - 4X - 10 = 0

4X = 200

X* = 50

Price = 210 - 2*50 = $110

Profit = 210*50 - 2*(50^2) - 10*50 = 5000.

(j) How much output will Cargiltyre produce?

50 units

(k) What price will Cargiltyre charge for its product?

$110.

(l) How much profits will Cargiltyre make?

$5000.