Suppose that there is a monopoly that is described by the following information:
Demand curve for product: P = 11- (1/1000)Q
MC of production for firm: MC = 2 + (1/1000)Q
Total Cost of production for firm: TC = 2Q + (1/2000)Q2 + 1000
- Determine the profit maximizing quantity and price if this firm acts as a single price monopolist. Show your work.
- Determine the firm’s total revenue (TR), total cost (TC) and profit if it acts as a single price monopolist. Show your work.
- Determine the value of consumer surplus (CS), producer surplus (PS), and total surplus (TS) if this firm acts as a single price monopolist. Show your work.
- Determine the value of deadweight loss if this firm acts as a single price monopolist. Show your work.
Suppose that instead of acting as a single price monopolist, this firm acted as if it was operating in a perfectly competitive industry. Assume the following:
Market demand curve for product: P = 11- (1/1000)Q
Market supply curve for product: P = 2 + (1/000)Q
Total cost of production of good: TC = 2Q + (1/2000)Q2 + 1000
- If this firm operated as if it was a perfectly competitive market, what would be the market equilibrium price and market equilibrium quantity? Show your work.
- If this firm operated as if it was a perfectly competitive market, what would be the firm’s total revenue (TR’), total cost (TC’), and profit under these assumptions? Show your work.
- If this firm operated as if it was a perfectly competitive market, what would be the value of consumer surplus (CS’), producer surplus (PS’), and total surplus (TS’) under these assumptions? Show your work.
- If this firm operated as if it was a perfectly competitive market, what would be the value of deadweight loss under these assumptions? Explain your answer.
Answer:
- To find the profit maximizing output and price for the single price monopolist we need to set MC = MR. We know that MC = 2 + (1/1000)Q , but we need to find MR. Use the demand curve to get MR: recall that MR for the monopolist will have the same y-intercept as the demand curve provided the demand curve is linear and will have twice the slope of the demand curve. Thus, MR = 11 – (2/1000)Q. Here’s the solution:
2 + (1/1000)Q = 11 – (2/1000)Q
(3/1000)Q = 9
Q = 3000
To find the equilibrium price for the single price monopolist, substitute Q = 3000 into the demand equation: P = 11 – (1/1000)(30000) = $8 per unit of output.
B
TR = P*Q = ($8 per unit of output)(3000 units of output) = $24,000
TC = 2Q + (1/2000)Q2 + 1000 = 2(3000) + (1/2000)(3000)(3000) + 1000 = $11,500
Profit for single price monopolist = TR – TC = $24,000 – $11,500 = $12,500
C
CS = (1/2)($11 per unit of output – $8 per unit of output)( 3000 units of output) = $4500
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
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.
