Answer to Question #76634 in Microeconomics for Matt Champion

Question

Firms Tetra and Pak are the only producers of juice cartons (y). Both have the cost function:
C(y) = 2y²
The inverse demand function in the market for juice cartons is as follows:
P = 200 - 2y
Where P denotes the price of one juice carton.

A) Assume the firms behave according to the Cournot oligopoly model. Find the market equilibrium (outputs, prices and profits)

B) What would the market equilibrium be if firm Tetra behaved as a quantity leader instead, according to the Stackleberg model?

Answer 1

C(y) = 2y² 
P = 200 - 2y.
A) Assume the firms behave according to the Cournot oligopoly model. The market equilibrium output is:
y = y1 = y2.
If P = a - b*(y1 + y2) and C(y1) = c1*y, then:
y1 = (a - c1)/2b - 0.5y2,
y2 = (a - c2)/2b - 0.5y1,
y = y1 = y2 = (200 - 2)/(2*2) - 0.5y,
1.5y = 49.5,
y = 33 units.
Price P = 200 - 2*(33 + 33) = $68.
Profits are:
TP = TR - TC = 68*33 - 2*33^2 = $66.
B) If firm Tetra behaved as a quantity leader instead, according to the Stackleberg model, then:
y1 = (200 - 2)/(2*2) = 49.5 units.
y2 = (200 - 2)/(2*2) - 0.5*49.5 = 24.75 units.
P = 200 - 2*(49.5 + 24.75) = $51.5.
TP1 = 51.5*49.5 - 2*49.5^2 = -$2351.25.
TP2 = 51.5*24.75 - 2*24.75^2 = $49.5.