Suppose that demand and supply for a competitive market are as follows: Qd = 320 -...

Suppose that demand and supply for a competitive market are as follows:

Qd = 320 - P and Qs = -40 + 2P

What would be the price and output combination that would result if firms in this market merged together to become a profit maximizing monopolist? By how much would the price change from the competitive level?

Solutions

Expert Solution

When the market is competitive, the equilibrium is at the point where,

Qd = Qs

320 - P = -40 + 2P

3P = 320 + 40 = 360

P = 360 / 3 = $120

Thus, the competitive market price is $120.

When the market becomes monopoly:

Q = 320 - P

P = 320 - Q [This is inverse demand function]

TR = P * Q = 320Q - Q²

MR = 320 - 2Q

Then, the supply function is,

Q = -40 + 2P

2P = 40 + Q

P = 20 + 0.5Q = MC [ This is inverse supply function and it is also called MC function]

The monopoly profit maximizing condition is,

MR = MC

320 - 2Q = 20 + 0.5Q

2.5Q = 320 - 20 = 300

Q = 300 / 2.5 = 120

P = 320 - Q = 320 - 120 = $200

Thus, the competitive market price is $200.

It means the price increases by $80 (i.e., $200 - $120) from the competitive level.

Rahul Sunny answered 2 years ago

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