The Duopolists Carl and Simon Face a Demand Function for Pumpkins

question 55

Multiple Choice

The duopolists Carl and Simon face a demand function for pumpkins of Q = 2,200 - 400P, where Q is the total number of pumpkins that reach the market and P is the price of pumpkins.Suppose further that each farmer has a constant marginal cost of $1.50 for each pumpkin produced.If Carl believes that Simon is going to produce Q_s pumpkins this year, then the reaction function tells us how many pumpkins Carl should produce in order to maximize his profits.Carl's reaction function is

• A)R_C(Q_s)= 400 - Qs/2.
• B)R_C(Q_s)= 2,200 - 800Q_s.
• C)R_C(Q_s)= 800 - Qs/2.
• D)R_C(Q_s)= 2,200 - 400Q_s.
• E)R_C(Q_s)= 1,200 - Q_s.

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Definitions:

Rational Expression

An expression formed by the quotient of two polynomials, resembling a fraction in which both numerator and denominator are polynomials.

Simplify

The process of altering an expression or equation to its most basic form without changing its value.

Domain

In mathematics, the set of all possible input values for which a function is defined.

Rational Function

A function represented by the ratio of two polynomials, where the denominator is not zero.