A firm has discovered a new kind of nonfattening, non-habit-forming dessert called zwiffle. It doesn't taste very good, but some people like it and it can be produced from old newspapers at zero marginal cost. Before any zwiffle could be produced, the firm would have to spend a fixed cost of $F. Demand for zwiffle is given by the equation q = 20 - p. The firm has a patent on zwiffle, so it can have a monopoly in this market.

Question

Quizplus · Accepted Answer

To determine whether the firm will produce zwiffle, we need to compare the total revenue from selling zwiffle to the total cost of producing it.

Total Revenue = Price x Quantity = p x q = p(20 - p) = 20p - p^2

To find the maximum revenue, we take the derivative of the revenue function with respect to p and set it equal to zero:

dRevenue/dp = 20 - 2p = 0 
p = 10

So the optimal price for zwiffle is $10 per unit, and the corresponding quantity demanded is q = 20 - p = 10.

Total Cost = Fixed Cost + Variable Cost = F + 0 = F

Therefore, the condition for the firm to produce zwiffle is:

Total Revenue > Total Cost 
20p - p^2 > F 
20(10) - (10)^2 > F 
100 > F

Thus, the firm will produce zwiffle only if the fixed cost is less than or equal to $100 (choice B).

A Firm Has Discovered a New Kind of Nonfattening, Non-Habit-Forming