Determining Price and Output under Monopoly: Suppose demand function for monopoly is Q = 200-0.4Q

Price function is P= 1000-10Q

Cost function is TC= 100 + 40Q + Q²

Maximum profit is achieved where MR=MC

To find MR, TR is derived.

TR= (1000-10Q) Q = 1000Q-10Q²

MR = ∆TR/∆Q= 1000 – 20Q

MC = ∆TC/∆Q = 40 + 2Q

MR = MC

1000 – 20Q = 40 + 2Q

Q = 43.63 (44 approx.) = Profit Maximizing Output

Profit maximizing price = 1000 – 20*44 = 120

Total maximum profit= TR-TC= (1000Q – 10Q²) – (100+ 40Q+Q²)

At Q = 44

Total maximum profit = Rs. 20844