Suppose the demand function for widgets is Q(p) = 60 – p, and all firms that produce widgets have total cost function C(q) = 16 + q^3.a) Suppose that the market is perfectly competitive and there is free entry and exit. All firms that enter use the same technology. A firm that decides to stay out of the market can avoid paying the fixed cost and has a profit of zero. Solve for the long-run competitive equilibrium. What is the long-run equilibrium price? What is the quantity produced by each firm? How many firms will produce in this market?b) What is the consumer surplus under the perfectly competitive model?

Question
Asked Feb 13, 2019
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Suppose the demand function for widgets is Q(p) = 60 – p, and all firms that produce widgets have total cost function C(q) = 16 + q^3
.
a) Suppose that the market is perfectly competitive and there is free entry and exit. All firms that enter use the same technology. A firm that decides to stay out of the market can avoid paying the fixed cost and has a profit of zero. Solve for the long-run competitive equilibrium. What is the long-run equilibrium price? What is the quantity produced by each firm? How many firms will produce in this market?

b) What is the consumer surplus under the perfectly competitive model?

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Expert Answer

Step 1

We are given the demand function for widgets as

Q(p) = 60 – p

And, the cost function is given as

C(q) = 16 + q3

Step 2

a) The long run competitive equilibrium is given by the condition (1).

Average Cost (AC): Average cost is the cost per unit of output.
Marginal Cost (MC): Marginal cost is the additional cost of producing an extra unit of output.
The long run competitive equilibrium is at the point where minimum of LAC, LMC, SAC and SMC coincide. There are only normal profits in the long run and all the costs are covered and there are no above normal profits. Hence, there is no incentive for the firms to enter or exit. Thus, it represents a stable equilibrium.
The long run competitive equilibrium has been illustrated in the following diagram.

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Step 3

Given the Cost, C(Q) =16+ q3

We calculate the Average Cost (AC)

...
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