Question

In: Economics

1. The following equation describes a firm’s total cost. TC = 500 + 10Q + Q2...

1. The following equation describes a firm’s total cost.

TC = 500 + 10Q + Q²

a. If the firm is a price taker and other firms in the industry sell output at a price of $100, what price should the manager of this firm put on the product?

b. What level of output should be produced to maximize profits (or minimize losses)?

c. Should the firm keep producing or shut down? Hint: Is P ≥ AVC?

d. Calculate profit (or losses)?

e. The firm sells orange juice, which is a perfect substitute, at a farmers market. What type of market is this firm operating in?

2. The following equations describe a firm’s demand and total cost.

P = 1,000 – 10Q

TC = 500 + 10Q + Q²

a. What level of output should be produced to maximize profits (or minimize losses)?

b. What is the market price?

c. Should the firm keep producing or shut down? Hint: Is P ≥ AVC?

d. Calculate profit (or losses)?

e. The firm sells cereal and competes with other firms selling slightly differentiated cereal products. What type of market is this firm operating in?

Solutions

Expert Solution

a. Since the firm is a price taker, it would sell at the same price at which the rest of the firms are selling. Hence price = $100.

b. Profit maximizing condition: Marginal Revneue = Price = Marginal Cost

MR = P = $100

MC = dTC/dQ = 2Q + 10

∴ 2Q + 10 = 100

Q = 45

c. Average Variable cost = TVC/Q

Total Cost = 500 +10Q + Q² = 500 + 10(45) + (45 × 45) = $2975

Total variable cost = Total cost - 500 = $2475

AVC = $2475 / 45 = $55

Since, P(=100) > AVC(=55), firms should continue to operate.

Total Revenue = P × Q = 100 × 45 = $4500

Total Cost = 500 +10Q + Q² = 500 + 10(45) + (45 × 45) = $2975

Profit = Total revenue - Total cost = $4500 - $2975 = $1525

The firm is in a perefectly competetive market. This is the market type where perfect substitutes are available and firms are price takers.

Profit maximizing condition: Marginal revenue = Marginal Cost

Total revenue = P×Q = (1000 - 10Q) × Q

MR = dTR/dQ = 1000 - 20Q

MC = dTC/dQ = 2Q + 10

∴ 2Q + 10 = 1000 - 20Q

Q = 45

b. P = 1000 - 10Q = 1000 - 10(45) = $550

Total Cost = 500 +10Q + Q² = 500 + 10(45) + (45 × 45) = $2975

Total variable cost = Total cost - 500 = $2475

AVC = $2975 / 45 = $55

Since, P(=550) > AVC(=55), firms should continue to operate.

Total Revenue = P × Q = 550 × 45 = $24750

Total Cost = 500 +10Q + Q² = 500 + 10(45) + (45 × 45) = $2975

Profit = Total revenue - Total cost = $24750 - $2975 = $21775

The firm is in a monopolistically competetive market. This is the market type where each firm sells a slightly differentiated product.

Rahul Sunny answered 1 year ago

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