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Assume that two firms operate in a market which has a demand function Q = 12 - 1

ID: 1209627 • Letter: A

Question

Assume that two firms operate in a market which has a demand function Q = 12 - 1P. Firm 1's output is designated by q1 and firm's 2's output is designated by q2. Because there are only two firms, the output on the market Q is equal to the sum of the two firms' outputs q1 and q2 respectively. It is important to note that, in this market, each of the two firms has a substantial impact on the market price. It is not like the model of pure competition where there are a sufficiently large number of firms that each firm has such a negligible impact on price that it takes the market price as given.

Derive an expression for the total revenue function of firm 1 given that firm 2 produces an output equal to 4 units.

a) TR1 = 8 – q1

b) TR1 = 8q1 – q12

c) TR1 = 12 – Q

d) none of the above

Explanation / Answer

Q = q1 +q2 where q2 = 4

Q = q1 + 4

Q = 12 - 1P

P = 12 -(q1 + 4)

P = 8 -q1

TR1 = Px q1

TR1 = 8q1 -q12

Answer is b) TR1 = 8q1 – q12