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1 Market Demand Molly W. Dahl Georgetown University Econ 101 – Spring 2009
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2 From Individual to Market Demand Functions Consumer i’s demand for commodity j Market demand for commodity j
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3 From Individual to Market Demand Functions The market demand curve is the “horizontal sum” of the individual consumers’ demand curves. Suppose there are only two consumers, i = A,B.
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4 From Individual to Market Demand Functions p1p1 p1p1 2015 p1’p1’ p1”p1” p1’p1’ p1”p1”
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5 From Individual to Market Demand Functions p1p1 p1p1 p1p1 2015 p1’p1’ p1”p1” p1’p1’ p1”p1” p1’p1’
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6 From Individual to Market Demand Functions p1p1 p1p1 p1p1 2015 p1’p1’ p1”p1” p1’p1’ p1”p1” p1’p1’ p1”p1”
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7 From Individual to Market Demand Functions p1p1 p1p1 p1p1 2015 35 p1’p1’ p1”p1” p1’p1’ p1”p1” p1’p1’ p1”p1” The “horizontal sum” of the demand curves of individuals A and B.
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8 Elasticities Elasticity measures the “sensitivity” of one variable with respect to another. The elasticity of variable X with respect to variable Y is
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9 Own-Price Elasticity pipi Xi*Xi* pi’pi’ What is the own-price elasticity of demand in a very small interval of prices centered on p i ’? is the elasticity at the point
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10 Own-Price Elasticity Consider a linear demand curve. If p i = a – bX i then X i = (a-p i )/b and Therefore,
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11 Own-Price Elasticity pipi Xi*Xi* p i = a - bX i * a a/b
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12 Own-Price Elasticity pipi Xi*Xi* p i = a - bX i * a a/b
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13 Own-Price Elasticity pipi Xi*Xi* a p i = a - bX i * a/b a/2 a/2b
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14 Own-Price Elasticity pipi Xi*Xi* a p i = a - bX i * a/b a/2 a/2b
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15 Own-Price Elasticity pipi Xi*Xi* a p i = a - bX i * a/b a/2 a/2b own-price elastic own-price inelastic own-price unit elastic
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16 Revenue, Price Changes, and Own-Price Elasticity of Demand Inelastic Demand: Raising a commodity’s price causes a small decrease in quantity demanded Sellers’ revenues rise as price rises. Elastic Demand: Raising a commodity’s price causes a large decrease in quantity demanded Seller’s revenues fall as price rises.
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17 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is
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18 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is So
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19 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is So
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20 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is So
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21 Revenue, Price Changes, and Own-Price Elasticity of Demand so ifthen and a change to price does not alter sellers’ revenue.
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22 Revenue, Price Changes, and Own-Price Elasticity of Demand but ifthen and a price increase raises sellers’ revenue.
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23 Revenue, Price Changes, and Own-Price Elasticity of Demand And ifthen and a price increase reduces sellers’ revenue.
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24 Revenue, Price Changes, and Own-Price Elasticity of Demand In summary: Own-price inelastic demand: price rise causes rise in sellers’ revenue. Own-price unit elastic demand: price rise causes no change in sellers’ revenue. Own-price elastic demand: price rise causes fall in sellers’ revenue.
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25 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand A seller’s marginal revenue is the rate at which revenue changes with the number of units sold by the seller.
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26 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand p(q) denotes the seller’s inverse demand function (i.e., the price at which the seller can sell q units). Then so
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27 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand and so
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28 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand says that the rate at which a seller’s revenue changes with the number of units it sells depends on the sensitivity of quantity demanded to price; i.e., upon the of the own-price elasticity of demand.
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29 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand Ifthen Ifthen Ifthen
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30 Selling one more unit raises the seller’s revenue. Selling one more unit reduces the seller’s revenue. Selling one more unit does not change the seller’s revenue. Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand Ifthen Ifthen Ifthen
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31 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand An example with linear inverse demand. Then and
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32 Marginal Revenue and Own-Price Elasticity of Demand a a/b p qa/2b
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