Suppose that each of a firm’s customers has the following demand curve: P = 20 –

Question

Suppose that each of a firm’s customers has the following demand curve: P = 20 – 2Q. Suppose also that the firm’s total cost function is TC = 8Q. The firm is considering three pricing strategies. Strategy 1: A single per unit fee. (No entrance fee) Strategy 2: An entrance fee with no per unit charge. Strategy 3: An entrance fee and a per unit fee equal to marginal cost. I. Strategy 1: A single per unit fee. (No entrance fee) a. Determine the firm’s total revenue function. (Note that this function is actually the total revenue from each customer, since the demand curve was for each customer.) b. Determine the marginal revenue (per customer) function. c. Determine the marginal cost function (“per unit sold to a customer.” Because the marginal cost is a constant, the cost of supplying one more unit to a given customer does not depend on how many customers there are or how much other customers buy). d. Set marginal revenue equal to marginal cost to determine this strategy’s profitmaximizing output level (per customer). e. Determine the profit-maximizing price using this strategy. f. Determine the total revenue per customer at the price and quantity found in parts d and e above. g. Determine the total cost per customer at the output level in part d above. h. Determine the profit that the firm will make from each customer. II. Strategy 2: An entrance fee with no per unit charge. a. Use the demand curve equation to determine how much each customer will purchase if there is no per unit charge (that is, P = 0). b. Determine the consumer surplus that the firm can charge each customer as an entrance fee when price is zero. c. What is the total cost per customer at the quantity consumed by each customer in part a? d. Determine the profit that the firm will make from each customer. (Remember that the total revenue per customer will be the entrance fee since there is no per unit charge.) III. Strategy 3: An entrance fee and a per unit fee equal to marginal cost. a. What is the marginal cost and therefore the price charged per unit based on this strategy? b. At the price found in part a, what quantity will each customer purchase? c. Determine the firm’s revenue per customer from the per unit charge, using the answers to parts a and b. d. Determine the consumer surplus that the firm can charge each customer as an entrance fee. e. Determine the total revenue from each customer using the answers to parts c and d. f. Determine the total cost at the quantity found in part b. g. Determine the profit that the firm will make from each customer. IV. Which of the three strategies will provide this firm with the greatest profit per customer?

Explanation / Answer

we have demand curve = P = 20 -2Q

and TC = 8Q

1)

A) TR = P * Q

Tr = (20-2Q) * Q

TR = 20Q - 2Q2

B) MArginal revenue function can derived by do differntiate of TR fucntion with respect to Q

TR = 20Q - 2Q2

So, MR = 20 - 4Q

C) Marginal cost is also derived by do differentitate of TC function with respect to Q.

TC = 8Q

So, MC = 8

D) Now MR =MC,

20-4Q = 8

12= 4Q or Q = 3

so, profit maximing output = 3

E) P = 20- 2*3 or P = 20-6= 14

so profit maximing price = $14

F) TR = P *Q = 14 * 3 = $42.

G) TC = 8Q = 8*3 =$24

H) Profit = TR-TC = 42 -24 = 18

so, profit = $18.

question 2. please upload it again with mention. its again chegg policy.

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