Suppose the demand for bicycles is given byQp = 10,000P- and the supply of bicycles isgiven by Qs = 0.01P3.(a) Using calculus and the given supply and demand curves, find mathematical expressionsfor the elasticities of demand and supply as a function of the price. Use these expressionsto demonstrate that both curves have constant elasticity along their entire length.(b) Find the equilibrium price and quantity in this market mathematically.

Answered: 10,000P-3 and the supply of bicycles is…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose the demand for bicycles is given byQp = 10,000P- and the supply of bicycles is
given by Qs = 0.01P3.
(a) Using calculus and the given supply and demand curves, find mathematical expressions
for the elasticities of demand and supply as a function of the price. Use these expressions
to demonstrate that both curves have constant elasticity along their entire length.
(b) Find the equilibrium price and quantity in this market mathematically.

Expert Solution

Step 1

Elasticity measures the responsiveness of quantity to changes in price.
Elasticity of demand is the percentage change in quantity demanded due to percentage change in price.
Elasticity of supply is the percentage change in quantity supplied due to percentage change in price.

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