Question

In: Economics

3) Suppose the demand curve for a particular product is given by Qd(P) = 600 –...

3) Suppose the demand curve for a particular product is given by Q^d(P) = 600 – 20P. Suppose also that marginal revenue and marginal cost to a monopolist is described by the following two equations. Suppose price is measured in $/lb and quantity is measured in lbs.

MR = 30 – (1/10)Q

MC = (1/5)Q

a) Determine the profit maximizing quantity, price, total revenue, and consumer surplus in this monopoly market.

Expert Solution

Profit is maximized where marginal revenue and marginal cost

Equating MR and MC

30 - (1/10)Q = (1/5)Q

30 = Q/5 + Q/10

300 = 3Q

Q = 100

Hence the profit-maximizing quantity is 100 units

To find the profit-maximizing price we will use this quantity in demand function.

Q = 600 - 20P

100 = 600 - 20P

P = 25

Hence the profit-maximizing price is $25

To find the total revenue we will use this formula

Total Revenue = Price x Quantity

Total Revenue = 25 x 100

Total Revenue = 2500

Hence the total revenue is $2500

The red triangle in the above graph represents the consumer surplus hence the area of this triangle will be equal to consumer surplus.

Consumer Surplus = 1/2 x base x height

Consumer Surplus = 1/2 x 100 x 5

Consumer Surplus = 250

Hence the consumer surplus is $250

Rahul Sunny answered 2 years ago

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