Suppose that the demand for a special kind of silica is given by Q = 55...

Suppose that the demand for a special kind of silica is given by Q = 55 – 0.5P, where Q is in tons of silica per day and P is the price per ton. This special kind of silica is produced by Thorpe Industries (a monopolist) that has a constant marginal and average total cost of $10 per ton.
1. Derive the inverse demand and marginal revenue curves faced by Thorpe Industries.
2. Equate marginal cost and marginal revenue to determine the profit-maximizing level of output.
3. Find the profit maximizing price for Thorpe Industries.
4. How would your answer change if marginal cost were instead given by MC = 10+Q?

Solutions

Expert Solution

a) Q= 55-0.5P

0.5P = 55-Q

P = 110-2Q

MR = 110-4Q

b) 110-4Q = 10

110-10 = 4Q

Q = 100/4 = 25

c) P = 110-2*25 = 60

d) IF MC = 10+Q

110-4Q = 10+Q

110-10 = Q+4Q

100 = 5Q

Q = 100/5 = 20

P = 110-2*20 = 70

Rahul Sunny answered 1 year ago

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