Price Elasticity of Demand. Overheads. How much would your roommate pay to watch a live fight?. How does Showtime decide how much to charge for a live fight?. What about Hank and Son’s Concrete?. How much should they charge per square foot?.

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Price Elasticity of Demand

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What about Hank and Son’s Concrete? How much should they charge per square foot? Can ISU raise parking revenue by raising parking fees? Or will the increase in price drive demand down so far that revenue falls?

The Law of Demand The law of demand states that when the price of a good rises, and everything else remains the same, the quantity of the good demanded will fall. The real issue is how far it will fall.

P Q Q P 0 100 1 99.5 2 99 3 98.5 4 98 5 97.5 6 97 7 96.5 8 96 9 95.5 10 95 11 94.5 12 94 13 93.5 14 93 Consider data on racquets Let P change from 95 to 96 P = 96 - 95 = 1 Q = 8 - 10 = -2 A $1.00 price change when P = $95.00 is tiny

Graphically for racquets Demand for Racquets 102 Price 100 98 96 Slope = - 1/2 94 92 90 88 0 2 4 6 8 10 12 14 16 18 Large % change in Q Quantity Small % change in P

Graphically for hand balls Demand for Handballs 11 Price 10 P = 7 - 6 = 1 9 8 7 6 Q = 6 - 8 = -2 P 5 4 3 Slope = - 1/2 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 Quantity Large % change in Q Large % change in P

So slope is not such a good measure of responsiveness Instead of slope we use percentage changes The ratio of the percentage change in one variable to the percentage change in another variable is called elasticity

Q P Price Elasticity of Demand (Final Point Method) P Q 6 8 5.5 9 5 10 4.5 11 4 12

The answer is very different depending on the choice of the base point So we usually use The midpoint method for computing The Own Price Elasticity of Demand

Classification of the elasticity of demand Inelastic demand When the numerical value of the elasticity of demand is between 0 and -1.0, we say that demand is inelastic.

Classification of the elasticity of demand Unitary elastic demand When the numerical value of the elasticity of demand is equal to -1.0, we say that demand is unitary elastic.

Elasticity of demand with linear demand Consider a linear inverse demand function The slope is (-B) for all values of P and Q For example, The slope is -0.5 = - 1/2

Q P The slope is constant but the elasticity of demand will vary P Q 12 0 11.5 1 11 2 10.5 3 10 4 9.5 5 9 6 8.5 7 8 8 7.5 9 7 10 6.5 11 6 12 5.5 13 5 14 4.5 15 4 16 3.5 17 3 18

Q P The slope is constant but the elasticity of demand will vary P Q 12 0 11.5 1 11 2 10.5 3 10 4 9.5 5 9 6 8.5 7 8 8 7.5 9 7 10 6.5 11 6 12 5.5 13 5 14 4.5 15 4 16 3.5 17 3 18

P smaller Q larger The slope is constant but the elasticity of demand will vary A linear demand curve becomes more inelastic as we lower price and increase quantity The elasticity gets closer to zero

The slope is constant but the elasticity of demand will vary Q P Elasticity Expenditure 0 12 0 2 11 -23.0000 22 4 10 -7.0000 40 6 9 -3.8000 54 8 8 -2.4286 64 10 7 -1.6667 70 12 6 -1.1818 72 14 5 -0.8462 70 16 4 -0.6000 64 18 3 -0.4118 54 20 2 -0.2632 40 22 1 -0.1429 22 24 0 -0.0435 0

The slope is constant but the elasticity of demand will vary Q P Elasticity Expenditure 0 12 0 2 11 -23.0000 22 4 10 -7.0000 40 6 9 -3.8000 54 8 8 -2.4286 64 10 7 -1.6667 70 12 6 -1.1818 72 14 5 -0.8462 70 16 4 -0.6000 64 18 3 -0.4118 54 20 2 -0.2632 40 22 1 -0.1429 22 24 0 -0.0435 0

Note We do not say that demand is elastic or inelastic ….. We say that demand is elastic or inelastic at a given point

The Own Price Elasticity of Demand and Total Expenditure on an Item How do changes in an items price affect expenditure on the item? If I lower the price of a product, will the increased sales make up for the lower price per unit?

Expenditure for the consumer is equal to revenue for the firm Revenue = R = price x quantity = PQ Expenditure = E = price x quantity = PQ