Market Demand and Revenue in Microeconomics: A Comprehensive Guide, Slides of Microeconomics

Download Market Demand and Revenue in Microeconomics: A Comprehensive Guide and more Slides Microeconomics in PDF only on Docsity!

Microeconomics

Market demand and revenue

Harald Wiese Leipzig University

Structure

Introduction Household theory Budget Preferences, indifference curves, and utility functions Household optimum Comparative statics Decisions on labor supply and saving Uncertainty Market demand and revenue Theory of the firm Perfect competition and welfare theory Types of markets External effects and public goods Pareto-optimal review

Prohibitive price and satiation quantity

Definition (prohibitive price)

Price for which demand is just zero

Definition (satiation quantity)

Quantity demanded at price zero

Aggregation of individual demand curves

 



 



 



Note prohibitive prices! Horizontal aggregation!

Demand function and price elasticity I

X

no reaction of demand

limited reaction of demand

demand can be any amount

Demand function and price elasticity II

Definition (price elasticity)

ε X ,p =

dX X dp p

dX dp

p X

By how many percent does demand change if the price increases by 1 percent? Inelastic demand | ε X ,p | < 1 Elastic demand | ε X ,p | > 1

Expenditures and revenue

Price times quantity from the household’s perspective: expenditures from the firm’s perspective: revenue

Revenue for demand function X (p):

R(p) = pX (p)

Revenue equals 0 at the prohibitive price (why?) and at the satiation quantity (why?).

Revenue curve and a question I

X , R

p

d

de

X

de p R max (^)  2

R

p?

Problem

What is the economic interpretation of the price p??

Marginal revenue with respect to price

Revenue for demand function X (p):

R(p) = pX (p)

Marginal revenue ( = MR, here MRp):

MRp = dR dp = X + p dX dp (product rule)

If the price increases by one unit, revenue increases by X (for every unit sold the firms obtain one Euro) revenue decreases by p dXdp (the increase in price decreases demand that is valued with the price)

Marginal revenue and price elasticity

Problem

Confirm the Amoroso-Robinson relation dR dp = X ( 1 + ε X ,p ) = −X (| ε X ,p | − 1 )!

Problem

What is the price elasticity of demand if revenue reaches its maximum?

Inverse demand function

Problem

Determine the inverse demand function for X (p) = 100 − 2 p.

Problem

Confirm that average revenue is equal to the price (revenue equals R (X ) = p (X ) X ).

Problem

Do you recognize p ( 0 ) and X ( 0 )?

Linear inverse demand function

A problem

Problem

Assume the linear inverse demand function p (X ) = a − bX , a, b > 0, and determine (^1) the slope of the inverse demand function (^2) the slope of marginal revenue dR (X ) /dX (^3) the satiation quantity and (^4) the prohibitive price

Again: price elasticity of demand

X









no reaction of demand

limited reaction of demand

demand can be any amount

ε X ,p =

dX X dp p

dX dp

p X

Again: price elasticity of demand

Problem

Calculate price elasticity of demand for the linear demand function p (X ) = a − bX! Which price and which quantity yields an elasticity of -1? Which price yields an elasticity of zero?

Inelastic demand | ε X ,p | < 1 Elastic demand | ε X ,p | > 1