Question

A firm is considering whether to introduce a new product. No other firms are considering producing the product. The product costs F to introduce and can be produced at zero marginal cost once the firm has spent F. If the firm introduces the product, it must charge the same per-unit price to all customers. The demand for the product is D(p) = 10 - p where p is price.

a.(10 pts) Are there values of F such that the firm would not introduce the product even though it would be socially optimal to have the product produced? If not, explain. If so, what are the values of F such that the firm does not introduce the product when a social planner would?

b.(10 pts) Consider the following extension of the problem. Suppose that the buyer is a single customer, e.g., a big downstream producer that earns surplus by selling in a final market (although you do not need to analyze activities in the final market to answer this question). Suppose the seller can charge the buyer a fixed fee K in addition to a per unit price p. In this case, are there values of the fixed cost F such that the seller will fail to introduce the product when it would be socially optimal to do so? Explain your answer with reference to the concepts of "business stealing" and "incomplete appropriation."

Answer 1

Step-by-step explanation:

a. Should in case the firm decides to introduce the new product, the total cost sum of variable and fixed cost if F, the variable cost is zero.

The firm could get a total revenue expressed as TR=P*Q=(10-Q)*Q=10Q-Q^2. The marginal revenue is 10-2Q. The marginal cost is 0. Thus, social optimal quantity can be calculated by equating marginal revenue to marginal cost.

MR=MC

10-2Q=0

2Q=10

Q*=5

Hence, the socially optimal quantity is 5.

However, if fixed cost is high enough such that the total profit for the firm is less than zero, the firm will not introduce the product in the market.

Total Profit=Total Revenue-Total cost

=(10-5)*5-F

=25-F

if F>25 then the firm will earn a negative profit, therefore, it will not introduce the product in the market.

B)

The negative effect created on the demand of competitor's goods when the firm changes its price strategy is referred to as business stealing.

If the firm chooses to introduce the new product the total cost sum of variable and fixed cost if F as variable cost is zero. The Total revenue the firm could get is TR=P*Q+K=(10-Q)*Q+K=10Q-Q^2+K. The marginal revenue is 10-2Q. The marginal cost is 0. Therefore socially optimal quantity can be calculated by equating marginal revenue to marginal cost.

MR=MC

10-2Q=0

2Q=10

Q*=5

Therefore, the socially optimal quantity is 5.

However, if fixed cost is high enough such that the total profit for the firm is less than zero, the firm will not introduce the product in the market.

Total Profit=Total Revenue - Total cost

= (10-5)*5+K-F

Total Profit = 25 + K - F

The firm will earn a negative profit if F > 25 + K, thus, it will not introduce the product in the market.

Now if the Fixed cost lies between 25 and 25+K, it will be beneficial for the firm to introduce the product. But the amount the per-unit price buyer has to pay will be P + K/Q.