2. Del Boy has discovered a new venture where he reckons that he can make high p
ID: 1113181 • Letter: 2
Question
2. Del Boy has discovered a new venture where he reckons that he can make high profits. He has discovered a secret pure mountain spring water source, which he reckons can be bottled and sold. The cost of producing the mountain water is zero. The market demand for this bottled spring water, called Peckham Pure, is given by: P 24-Q (a) Find out the profit maximising output level and price for a monopolist der the case of a Cournot duopoly, Derive the equations for the reaction functions for each firm. In the long-run what level of output would be produced by each firm? At what price will this output sell? (c) If this industry was perfectly competitive, what would be the equilibrium price and output? Compare this output level with that under duopoly and under monopoly.Explanation / Answer
We are given that MC = 0. From demand function P = 24 - Q, we infer that MR = 24 - 2Q
a) For a monopolist, profit maximizing output is found by MR = MC
24 - 2Q = 0
Qm = 12 and Pm = 24 - 12 = $12
This is the price quantity combination for a monopolist
b) Since MC = 0, marginal revenue functions are best response or reaction functions
MR1 = 0 MR2 = 0
24 - 2Q1 - Q2 = 0 24 - 2Q2 - Q1 = 0
Q1 = 12 - 0.5Q2 and Q2 = 12 - 0.5Q1
Solve them to get Q1 = Q2 = 8 units. Uniform long run price is P = 24 - (8+8) = $16
c) Perfect competition has P = MC for profit maximization
24 - Q = 0
Q* = 24. Now this seems irrational because marginal cost is zero so effectively price is zero. But no firm produces anything it recives nothing in return. We however see that price is highest in monopoly and lowest in perfectly competitive market. Output is produced lowest in monopoly and highest in perfectly competitive market
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