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Market Demand increasing profit

QUESTION : Market demand is given as QD = 200 – 3P. Market supply is given as QS = 2P + 100. Each identical firm has MC = 0.5Q and ATC = 0.25Q. What is each firm’s profit?

SAMPLE ANSWER : Profit = Total revenue – Total cost

Step 1: To find Total revenue

If we equate the Market demand and market supply, we will get the equilibrium price and quantity. Accordingly,

200 – 3P = 2P + 100

200 – 100 = 2P + 3P

100 = 5P

P = 100/5 = $20

If price = $20, then the total revenue = P x Q = 20Q

QUESTION : A monopolist faces market demand given by P = 200 – Q. For this market, MR = 200 – 2Q and MC = 3Q. What quantity of output will the monopolist produce in order to maximize profits?

SAMPLE ANSWER :

Profits are maximized at the point where MR = MC.

We have to therefore equate MR and MC.

MR = 200 – 2Q & MC = 3Q

200- 2Q = 3Q

200 = 5Q

Q = 200/5 = 40 units. This is the profit maximizing output.

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