Imagine a population of bachelors and parents. Costco wants to sell mustard in t

Question

Imagine a population of bachelors and parents. Costco wants to sell mustard

in this world (85 gallon jugs of mustard or something). The parents’ demand is given by

Qp = 7 2P , while the bachelors’ demand is given by Qb = 93P . The marginal cost of 2

producing mustard is $1 per jug. What is the optimal way of selling this mustard? Consider simple monopoly pricing for the aggregate demand vs. two part tariffs. Assume first that there is one parent and one bachelor, then solve the problem again, considering 1 parent and 5 bachelors. ( = 18.2)

Explanation / Answer

Qp = 7-2P

P = 3.5-Qp/2

MR = 3.5-Qp

At equilibrium MR = MC

3.5-Qp = 1

Qp = 2.5

Price = $1

For bachlers

Qb = 9-3P

P = 3-Qb/3

MR = 3- 2Qb/3

At equilibrium

MR = MC

3- 2Qb/3 = 1

9-2Qb = 3

2Qb = 6

Qb = 3

Price = 3-3/3 = 3-1 =$ 2

Profit = AR-AC

Profit for parents = 1-1 = 0

Profit for bachelors' = 2-1 = 1

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