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.
A)The firm will not produce zwiffle if F 20.
B)The firm will produce zwiffle only if F is less than or equal to 100.
C)The firm will produce 15 units of zwiffle.
D)The firm will produce 20 units of zwiffle.
E)None of the above.

Question

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.
A)The firm will not produce zwiffle if F > 20.
B)The firm will produce zwiffle only if F is less than or equal to 100.
C)The firm will produce 15 units of zwiffle.
D)The firm will produce 20 units of zwiffle.
E)None of the above.

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 zwiffle. Total revenue is given by p*q, which we can rewrite using the demand equation as p*q = F*(F1^2*S1)/(F1^2 + 20*F1 - F). Total cost is simply the fixed cost F since the marginal cost of producing zwiffle is zero.

Therefore, the condition for the firm to produce zwiffle is:
F*(F1^2*S1)/(F1^2 + 20*F1 - F) - F > 0
Simplifying this inequality, we get:
F > F1^2*S1/(F1^2 + 20*F1 - 2*F)

Substituting F = 100 into this inequality, we get:
100 > F1^2*S1/(F1^2 + 20*F1 - 2000)
Multiplying both sides by (F1^2 + 20*F1 - 2000), we get:
100*(F1^2 + 20*F1 - 2000) > F1^2*S1
Expanding the left-hand side, we get:
100F1^2 + 2000F1 - 200000 > F1^2*S1
Dividing both sides by F1^2, we get:
100 + 2000/F1 - 200000/F1^2 > S1
Since S1 is positive, we can conclude that the firm will produce zwiffle only if 100 + 2000/F1 - 200000/F1^2 > 0, or equivalently, if F <= 100. Therefore, the answer is B.

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