14. Suppose that a firm has a monopoly on a good with the following demand sched
ID: 1250390 • Letter: 1
Question
14. Suppose that a firm has a monopoly on a good with thefollowing demand schedule:
Price Quantity Price Quantity
$10 0 $4 6
$ 9 1 $3 7
$ 8 2 $2 8
$ 7 3 $1 9
$ 6 4 $0 10
$ 5 5
a. What price and quantity will the monopolist produce at if the marginal cost is a
constant $4?
b. Calculate the deadweight loss from having the monopolist produce, rather than a
perfect competitor.
Explanation / Answer
You need to calculate the total revenue (TR) and marginal revenue (MR) from each level of output. TR = P*Q; MR = (TR from this quantity - TR from one less). Here's what a table would look like (I know this isn't neat): P, Q, TR, MR 10, 0, 0, 0 9, 1, 9, 9 8, 2, 16, 7 7, 3, 21, 5 6, 4, 24, 3 5, 5, 25, 1 4, 6, 24, -1 3, 7, 21, -3 2, 8, 16, -5 1, 9, 9, -7 a. The monopolist would keep producing as long as MR >= MC. With a constant MR=4, he would produce the 3rd unit (but not the 4th). b. A competitive firm would have produced until MC = Price, so it would have produced 6 units at a price of 4 apiece. The lost consumer surplus is the difference between a consumer's willingness to pay (given by the demand curve) and the price, for all of those "unproduced" units. From the 4th: ($6 - $4) = $2. From the 5th unit: $5 - $4 = $1. From the 6th: $4-$4 = 0. Altogether, it's $2 + $1 + $0 = $3 of deadweight loss.
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