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PS = (1/2)($5 per unit of output - $2 per unit of output)(3000 units of output) + ($8 per unit of output - $5

per unit of output)(3000 units of output) = $4500 + $9000 = $13,500

TS = CS + PS = $4500 + $13,500 = $18,000

d. DWL = (1/2)($8 per unit of output - $5 per unit of output)(4500 units of output – 3000 units of output)

= $2250

e. To find the market equilibrium set the market demand curve equal to the market supply curve:

11 – (1/1000)Q’ = 2 + (1/1000)Q’

9 = (1/500)Q’

Q’ = 4500 units of output

Use either the market demand curve or the market supply curve to find the market equilibrium price if the

firm acts as if this is a perfectly competitive market:

P’ = 11 – (1/1000)Q’ = 11 – (1/1000)(4500 units of output) = $6.50 per unit of output

Or, P’ = 2 + (1/1000)Q’ = 2 + (1/1000)(4500 units of output) = $6.50 per unit of output

f. TR’ = P’*Q’ = ($6.50 per unit of output)(4500 units of output) = $29,250

TC’ = 2(4500) + (1/2000)(4500)(4500) + 1000 = $20, 125

Profit if the firm acts like this is a perfectly competitive market = $9125

g. CS' = (1/2)(11 – 6.5)(4500) = $24,750/2 = $10,125

PS' = (1/2)(6.5 – 2)(4500) = $20250/2 = $10,125

TS' = (1/2)(11 – 2)(4500) = $40500/2 = $20,250

Or, TS' = PS' + CS' = $10,125 + $10,125 = 20,250

h. There is no DWL if the firm produces 4500 units of output and sells them for $6.50 per unit of output

since at this level of production the MC of production is equal to the price that the good sells for. Recall

that when P = MC for the last unit sold, this tells us that the socially optimal amount of the good is being

produced.

4. Suppose you are given the following graph of a monopoly.

a. Given this graph, write an equation for this monopolist’s marginal revenue curve (MR).

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b. If this monopolist is a single price monopolist, what price and output will this monopolist produce?

What will be the monopolist’s profits at this price and output combination? Show how you found your

answers.

c. If this monopolist is instead regulated to produce the socially optimal amount of the good, what price

and output will the monopolist produce? What will the regulatory authority need to do in order to get the

monopolist to produce at this price and output level? Explain your answer fully.

d. If this monopolist is instead regulated to produce at an output level where the firm breaks even, what

price and output will the monopolist produce? Is there a deadweight loss associated with this level of

production? Explain your answer verbally and then provide a mathematical calculation of this area of

deadweight loss.

Answer:

a. From the graph it is relatively easy to write the monopolist’s demand curve: P = 100 – (1/1000)Q. Once

we have the demand curve, then we can write the monopolist’s MR by recalling that MR for the

monopolist will have the same y-intercept as the demand curve and twice the slope: thus, MR = 100 –

(1/500)Q.

b. If the monopolist is a single price monopolist it will produce that quantity where MR = MC and then

charge the price associated with this quantity and the demand curve. So, looking at the graph we can find

MR (see (a)): MR = 100 – (1/500)Q but we cannot write an equation for MC. But, we know from the

graph that MR = MC when MC is $40 per unit. So, we can set MC = MR and substitute 40 for MC: thus,

40 = 100 – (1/500)Q or Q = 30,000. Then using this quantity and the demand curve we can find the price

this monopolist will charge: P = 100- (1/000)(30,000) = $70 per unit. The monopolist will produce 30,000

units and charge a price of $70 per unit if the monopolist is a single price monopolist that is not regulated.

To find the monopolist’s profits we need to recall that profits = TR – TC. TR = P*Q = ($70 per unit)

(30,000 units) = $2,100,000. TC we need to find by looking at the graph and finding the ATC for 30,000

units and then recalling that TC = ATC*Q. So, TC = ($60 per unit)(30,000 units) = $1,800,000. Profits

are therefore equal to $300,000.

c. If the monopolist is regulated to produce the socially optimal amount of the good, the monopolist will

produce that amount of good where P = MC: from the graph we can see that P = MC where the MC curve

intersects the demand curve. This occurs at a quantity of 85,000 units (quite a bit more than that single

price monopolist was going to produce!). To find the regulated price we will need to go back to the

demand curve and substitute Q = 85,000 into it since we do not have an equation for the MC curve: thus,

P = 100 – (1/1000)(85,000) = $15 per unit (quite a bit lower than the price the single price monopolist

was going to charge!). However, this regulated monopolist will be unwilling to produce at this price and

quantity combination without a subsidy since at the price and output, the firm earns negative economic

profit. From the graph it is impossible to measure the size of the subsidy needed, but we could write an

expression for the size of the subsidy as: Subsidy = (ATC of producing Qptimal – MC of producing

Qptimal)(Qptimal). See if you can find this area on the above graph.

d. If the monopolist is regulated to breakeven, the monopolist will produce that amount of good where P

= ATC: from the graph we can see that P = ATC where the ATC curve intersects the demand curve. This

occurs at a quantity of 60,000 units and a price of $40 per unit. There is a deadweight loss associated with

producing this level of output since P is greater than MC when the firm produces 60,000 units. The DWL

measures the total surplus that is given up in a market: this time this surplus is given up because of

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