Question

In: Economics

Firm A produces a product in high demand and it holds the sole legal authority to produce from patent protection.

Firm A produces a product in high demand and it holds the sole legal authority to produce from patent protection. The demand function is Qd=1,000,000-10P and the market supply curve is Qs=25P-125,000. The total cost function is C=$1,000,000,000+$5000Qs. Derived from C, we the marginal cost of the firm, MC=$5,000.

a. What would be the equilibrium quantity and price if this were a perfectly competitive market? Demonstrate graphically the consumer surplus, producer surplus

b. Now assume there is one firm (Firm A) in this sector, calculate the optimal quantity and price. Calculate the producer surplus, consumer surplus, and deadweight loss. Demonstrate your findings in a graph.

c. Now assume that a new firm (Firm B) with a product that fits an identical purpose for consumers. This firm faces the same costs as Firm A. Show how to determine the new equilibrium quantities for both firms and equilibrium prices. Show your results graphically.

d. How many firms would be viable in this market? In other words, how many firms would remain in the market in the long run? Does the market quantity and price approximate the competitive outcome? Why or why not? If not, what is the deadweight loss and how does it compare to the monopoly case?

 

Solutions

Expert Solution

a.

For Equillibrium quantity let equate Qd = Qs

1000000 - 10P = 25P - 125000

1125000 = 35P

P = 32142.86

Q = 678571.43

These will be P and Q for the figure below.

There will be no dead weight loss.

b.

Only one firm, this firm will try and maximise its profit

Equating MC = MR,

As per the above figure, (the slope of MR curve is double the slope of Demand curve)

As demand is Qd = 1000000 - 10P

MR should be

MR = 500000 - 5P

Now equating MC = MR for profit maximising

5000 = 500000 - 5P

P = 999000

c.

Cournot equillibrium will be applied in this scenario. As this market will be a duopoly in this case, when there are 2 firms. So both will product Q/3 and Q/3. Rest of the Q/3 will be lost. Here, Q is considered to be the total demand in the market. So, Q will be 1000000 from the demand curve equation.

This output is achieved using Cournot model where it is assumed that each firm looks at the production of the other firm and then tries to maximise its own profit. This process repeats itself and the final output for both is Q/3.

d.

More the number of firms, less will be the economic profit.

Maximum number of firms in the market will be derived when economic profit is set to zero.

So, Total Revenue = Total Cost


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