A firm's total cost of producing Q units of output is C (Q) = 200 +...

A firm's total cost of producing Q units of output is C (Q) = 200 + 50Q. The inverse demand curve for the firm's product is P(Q) = 80-Q, where P denotes the price of the product.

a) If the price of the product is set equal to the firm's average, how much will the firm produce? (5 points) Hint: choose the larger of the two numbers. Show your work.

b) If the firm is under marginal cost pricing, how many units will the firm produce? Show your work. (5 points)

Expert Solution

a) C(Q)= 200+50Q

Average Cost: AC(Q)=( 200/Q)+ 50

If Price is equal to Average Cost

P(Q)= AC(Q)

80–Q=( 200/Q)+50

80Q–Q2= 200+50Q

Q2+50Q–80Q+200= 0

Q2 –30Q+200= 0

Q= 20

The firm will Produce 20 units of Output if it keeps its price equal to Average Cost.

b) If Firm Keeps its Price equal to Marginal Cost, then

MC(Q)= 50= P(Q)

50= 80–Q

Q= 30.

The firm will produce 30 units of Output if firm is under Marginal Cost pricing.

Rahul Sunny answered 1 year ago

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