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Assignment - Monopoly and Perfect Competition Market
Demand for device: P = 50 - q where P is the price per unit and q is the quantity. Let MC = c = 25.
a. Suppose the industry is a monopoly. Find the equilibrium price, quantity, and profits of the industry.
Firm will maximize their profit, the profit function becomes
π = TR - TC
π = P. q - c. q
π = (50 - q). q - 25. q
Differentiating profit function w.r.t q
dπ/dq = 50 - 2q - 25
Putting f.o.c equal to zero dπ/dq = 0
q = 25/2
P = 50 - q
P = 50 - 25/2
P = 75/2
π = (50 - q). q - 25. q
Putting values of P and q in profit function
π = (625/2) - (625/4)
π = 625/4
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b. Suppose a technological breakthrough occurs which reduces the cost of manufacturing an c-book device. Find the new equilibrium price, quantity, and profits of the industry. How much did the monopoly gain from the innovation?
Suppose now the MC becomes 20 i.e. c' = 20
Then the firm (industry) will try to maximize its profit, the profit function becomes
π = TR - TC
π = P. q - c'. q
π = (50 - q). q - 20. q
Differentiating profit function w.r.t q
dπ/dq = 50 - 2q - 20
Putting f.o.c equal to zero dπ/dq = 0
q* = 15
P = 50 - q
P = 50 - 15
P* = 35
π = (50 - q). q - 20. q
Putting values of P* and q* in profit function
π* = 450 - 225
π* = 225
The profits from the introduction of new technology have increased.
π* - π = 225 - (625/4) = 68.75
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When the industry is perfectly competitive, the price in the market is equal to the marginal cost of the product produced and the economic profits in long run in perfectly competitive market is zero.
So, P = MC
When MC = 25,
50 - q = 25
q = 25
P = 25
π = 0
When MC' = 20
P = MC'
50 - q = 20
q* = 30
P* = 20
π = 0
c. Suppose the industry were perfectly competitive instead of a monopoly. We want to figure out what the gain from innovation is to an innovator in a competitive industry. So, first, find what the competitive industry's price, quantity, and profits would be initially. Then, imagine the same innovation has occurred, i.e. an innovator discovers a new method of producing e-book devices which reduces the constant marginal cost of production from 25 to 20. If the innovator licenses this technology to all the firms in the competitive industry, what royalty fee could the innovator charge per unit and what would be the total royalties the innovator could collect?
After the innovation of an innovator, the marginal cost for a perfectly competitive firm will be
MC' = 20 + RF
where RF is the royalty fee
Then according to marginal cost pricing under perfectly competitive firm, the new price for the firms will be
P = MC'
P = 20 + RF
50 - q = 20 + RF
RF = 30 - q
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The total royalties that the innovator could collect will be dependent on the quantities produced which is q
So the royalty charge will be RF.q = (30 - q).q
The innovator will try to maximize its royalties.
By differentiating royalties w.r.t q
dRF/dq = 30 - 2q
Putting f.o.c equal to zero
dRF/dq = 0
30 - 2q = 0
q = 15
To maximize royalties q = 15, then Royalty fee becomes
RF = 30 - q
RF = 15
And total royalties become
RF. q = 225
d. What can you say about which industry type (competition or monopoly) generates greater incentives for innovation?
The greater incentives for innovations are with the monopoly as the profits earned by them in the long run will be positive and with same marginal cost, they will be able to produce more, however, in perfect competition firm earns only normal profits, i.e. the economic profits are zero. With zero long run economic profits due to marginal cost pricing, it gets less incentivizing for the firms to adopt a new technology as any new technology requires more fixed cost to be invested in.
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