9. The demand function for a certain product is given by q = 500-2p. a. Is the demand function one-to-one? Explain why (not). If it is a one-to-one function, is the inverse function also a linear function? Explain why (not). b. Assume that the equation p = 21+0.4t describes how the price p changes in terms of the time t. Is the demand q a linear function of the time? Explain.

9. The demand function for a certain product is given by q = 500-2p. a. Is the demand function one-to-one? Explain why (not). If it is a one-to-one function, is the inverse function also a linear function? Explain why (not). b. Assume that the equation p = 21+0.4t describes how the price p changes in terms of the time t. Is the demand q a linear function of the time? Explain.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Elasticity of Demand and Supply

The elasticity of demand and supply are two important concepts of microeconomics. The elasticity of demand measures the responsiveness of consumers’ demands to the price change, changes in income of consumers, and changes in the price of the related goods. Similarly, the elasticity of supply refers to the proportionate change in the quantity supplied due to the proportionate change in the price. In other words, it can be said that elasticity of supply measures how the quantity of supply changes when the price changes of that particular product.

Question

can u solve point a to d?

9. The demand function for a certain product is given by q = 500 - 2p.
a. Is the demand function one-to-one? Explain why (not). If it is a one-to-one function, is the inverse
function also a linear function? Explain why (not).
b. Assume that the equation p = 21+0.4t describes how the price p changes in terms of the time t.
Is the demand q a linear function of the time? Explain.

Now assume that the demand function for a certain product q = f(p) is a non-constant general linear
function.
c. Is the function f necessarily a one-to-one function? Explain why (not). If it is a one-to-one
function, is the inverse of f again a linear function? Explain why (not).
d. Assume that the price p evolves as a non-constant linear function of the time t. Is the demand q
a linear function of the time? Explain.
The demand function for a second product, q = g(p), is a quadratic function.
e. Is the function g necessarily a one-to-one function? Explain why (not). If it is a one-to-one
function, is the inverse of g again a quadratic function? Explain why (not).
f. Assume that the price p evolves as linear function of the time t. Is the demand q a quadratic
function of the time? Explain.

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