[inao]

Description : The City of Pune has a hundred petrol Pumps selling identical products, but owned by different owners. The total market demand is given by
Q = 50000 - 20000P.
The total supply function is given by
Q = 25000P.
One of the Oil Companies decides to take all of these pumps. There is no apparent cost advantage because the cost function remains the same, regardless of whether it is one large company or many small ones.
The users of petrol are distributed and annoyed at this because they anticipate exploitation.
You are required to calculate the following:
(I) The price prior to merger
(ii) The price post merger
Note that the supply function is nothing but the rising part of the relevant cost function. If the government steps in and decides to regulate the price, would you recommend a marginal cost pricing regulation? Why or why not?
Discuss the ideal market structure, given the nature of the commodity.

[Curlyben]

What do YOU think ?
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[inao]

Please check this answer I have little confusion here...

I) In competitive case, supply = demand

Q = 50000 - 20000P
Q = 25000P
=> 50000 - 20000P = 25000P
=> 45000P = 50000
=> P = 50/45 = 1.111...



ii) "Note that the supply function is nothing b ut the rising part of the relevant cost function". The relevant cost function is the marginal cost function, so the supply function gives us the marginal cost function for the industry. P = (1/25000)Q = marginal cost.

Rearranging the demand curve so that P is the subject:
P = 5/2 - (1/20000)Q

The monopolist maximises profit by setting marginal revenue equal to marginal cost.

Total revenue is PQ = [5/2 - (1/10000)Q]Q = (5/2)Q - (1/20000)Q^2
Marginal revenue is the derivative wrt Q:
MR = 5/2 - (1/10000)Q

Set MR = MC

5/2 - (1/10000)Q = (1/25000)Q
(1/10000+1/25000)Q = 5/2
Q = 17857.14
Price = 5/2 - (1/20000)Q
P = 1.6

iii) This firm doesn't face the problem associated with the natural monopoly structure where marginal cost is below average variable cost, and so below the firm's shutdown point. As a caveat, in the real world it's almost impossible to know a firm's marginal cost function.

iv)The idea market structure is perfect competition, due to the product being homogeneous.