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

  


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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


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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)


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At Q = 44

Total maximum profit = Rs. 20844