Question

Monopoly problem: Find TR (total revenue), TC (total cost), P (price), Q (quantity), Profit & elasticity

Given: TC=10,000+100Q+0.20Q^2

Qd (demand)=20,000-10P

Answer 1

Monopoly Problem

From TC, we get MC = 100 + 0.40Q. Inverse demand is 10P = 20000 - Q or P = 20000/10 – Q/10 or P = 2000 – 0.1Q. Marginal revenue MR = 2000 – 0.2Q

Profit is maximized for a monopoly when MR = MC

2000 – 0.2Q = 100 + 0.4Q

1900 = 0.6Q

Q = 3166.667 and price P = 2000 – 0.1*3166.67 = $1683.333

Total revenue = PQ = 1683.333*3166.667 = $5,330,556

Total cost = 10000 + 100*3166.667 + 0.2*(3166.667^2) = $2,332,223.

Profit = TR – TC = $5,330,556 - $2,332,223 = $2,998,333