Profit maximizing single price monopoly. Demand for the product is given by: QD=50-2P; total cost: TC=10+6q+0.5q2...

Profit maximizing single price monopoly. Demand for the product is given by: Q_D=50-2P; total cost: TC=10+6q+0.5q²

a. Determine price he would charge as single price monopolist

b. calculate markup

c. determine quantity he would produce

d. calculate profit earned

Solutions

Expert Solution

a. Equating marginal revenue of the firm with the marginal cost of the firm:

P = 25-0.5Q

TR= 25Q- 0.5 Q2

MR= 25 - Q

MC = 6 + Q

25-Q = 6 + Q

Q = 19/2= 9.5 units and P =25 - 19 /4 = $20.25

b. P - MC / P = 0.306 = 0.31 approximately

c. Quantity produced = 9.5 units.

d. Total revenue = Price * Quantity = 20.25 * 9.5 = $192.375

Total cost at Q = 9.5 = 112.125

Profits = total revenue - total cost = $80.25

Rahul Sunny answered 1 year ago

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