Question

3.[2 points) A firm's short-run total cost is TC = 10,100 + 7, 700Q-100Q2 +Q3/3, and its marginal cost is MC = 7, 700-200Q+Q2. What is the firm's shutdown price? A) $45 B) $200 C) $1,100 D) $18 4.[2 points) Cravats inc., which sells bags designed by famous people, faces a demand curve of Q = 150 - 0.2P, where Q is measured in hundreds of bags and P is the price per bag. The marginal cost of production is given by MC = 5Q. What is Cravats' profit-maximizing output level? (Hint: Add two zeros to the number you get.) A) 25,000 B) 5,000 C) 450 D) 6,000 5.[2 points) A firm's demand curve is given by Q = 10-2P. What is the firm's corresponding marginal revenue curve? A) 10 - 4P B) 5-Q C) 10 - 4Q D) None of the above

Answer 1

Part 1) We have the following information

Total Cost (TC) = 10100 + 7700Q – 100Q² + Q³/3

Marginal Cost (MC) = 7700 – 200Q + Q²

Shutdown price is the price at which the average variable cost is equal to the price. The portion of the MC which is above the minimum point of AVC is the supply curve

Variable Cost (VC) = 7700Q – 100Q² + Q³/3

Average Variable Cost (AVC) = VC/Q = 7700 – 100Q +Q²/3

Taking the derivative of AVC

ΔAVC/ΔQ = – 100 + 2/3(Q)

Equating it to zero

– 100 + 2/3(Q) = 0

Q = 150

Taking the second derivative: Δ²AVC/ΔQ² = 2/3

So, the AVC is minimum at Q = 150

No, Price = MC = 7700 – 200Q + Q² is supply curve for quantities equal to or above 150

P = 7700 – 200Q + Q²

P = 7700 – (200 × 150) + (150)²

P = 7700 – 30,000 + 22,500

P = 30,200 – 30,000

Shutdown price is $200

Part 2) We have the following information

Demand curve: Q = 150 – 0.2P

Inverse demand curve: P = 750 – 5Q

Total Revenue (TR) = P × Q

TR = 750Q – 5Q²

Marginal revenue (MR) = ΔTR/ΔQ = 750 – 10Q

Marginal Cost (MC) = 5Q

The equilibrium is reached at the point where the MR is equal to the MC

750 – 10Q = 5Q

750 = 15Q

Q = 50

Equilibrium quantity (Q) = 5,000

Part 3) Demand curve: Q = 10 – 2P where P is price and Q is output

Inverse demand curve: P = 5 – 0.5Q

Total Revenue (TR) = P × Q

TR = 5Q – 0.5Q²

Marginal revenue (MR) = ΔTR/ΔQ = 5 – Q