Lecture 2

Elasticity

Costs

Perfect Competition

Elasticity

• Elasticity is a measure of how responsive the quantity demanded is to changes in environmental variables that determine demand.

• To make the measure units free, elasticity is calculated as the % change in quantity demanded per % change in a variable.

Own Price Elasticity

• For own price elasticity, the variable is product price.

• Own price elasticity is: % change in quantity demanded of X / % change in price of X.

• Own price elasticity is negative; demand is referred to as elastic if elasticity is greater than 1 (in absolute value), inelastic if it is less than 1 (in absolute value) and unitary elastic if elasticity equals -1.

Sales Revenue and Elasticity

• Why care about own price elasticity?

• If demand is elastic, then a price reduction increases sales revenue; if demand is inelastic, then a price rise leads to an increase in sales revenue.

Cross Price Elasticity

• Cross price elasticity measures how responsive quantity demanded is to changes in price of other goods.

• Cross price elasticity is: % change in quantity demanded of X / % change in price of Y.

• Often used to measure whether or not two goods are in same market

Income Elasticity

• Income elasticity measures how responsive quantity demanded is to changes in income.

• Income elasticity is: % change in quantity demanded of X / % change in income.

• If positive—normal good

• If negative—inferior good

Elasticity of Supply

• Elasticity of supply measures how responsive quantity supplied is to changes in its price.

• Elasticity of supply is: % change in quantity supplied of X / % change in price of X.

The Cost Function

• As the demand function summarizes the customer/sales side of the market, the cost function summarizes the production side of the market.

• What should costs depend on?– input prices (including price of raising capital)– quantity produced– Technology

Cost Function Cont’d

• Cost function properties:– Cost increasing in quantity produced– Cost increasing in input prices– Cost decreasing for technology

improvements.

• Cost can be divided into two components: a fixed cost component (F) and a variable cost component (c(x)).

Marginal and Average Cost

• Average cost gives cost per unit: C / x• Since price gives revenue per unit, price

relative to average cost determines if profits positive or negative

• Marginal cost gives the increase in costs due to an increase in quantity produced. Formally, marginal cost is the slope of the variable cost function.

The Marginal Cost Function

• The amount by which costs increase as quantity produced increases (i.e., marginal cost) may or may not vary with output

• We consider two cases:– constant marginal cost: c(x) = cx– increasing marginal cost

• The latter is typically viewed as the result of some input being in fixed supply

The Average Cost Function

• Average cost also varies with quantity produced: AC = C / x

• The way that average cost varies with x is determined by the way that marginal cost varies:– if c(x) = cx, then AC = F / x + c and so AC

declining with x if F > 0 and constant if F = 0– If c(x) increasing, then AC = F / x + c(x) / x.

AC is U – shaped if F > 0, increasing if F = 0

Market Structures

Perfect Competition

• Large numbers of “small” producers• Identical product• All firms are “price takers”• Free entry into and exit from market• Perfect information

Perfect Competition Cont’d

• Choose output such that PX = MC(x)

• Firm supply curve is that part of MC curve above AC. Market supply curve is sum of firm supply curves

• Entry/exit occurs until profits 0: PX = minX AC(x)