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Demand and Price Elasticity Example from the Firm Isoquants 16 1, 16 If this firm wants to produce 4 14 units of output, it should use 4 12 Q=4 units of labor and 4 units of capital. 10 Capital 8 6 4 4, 4 2 16, 1 0 0 2 4 8 6 Labor 10 12 14 16 • Firm Problem: – For a given quantity, find the least cost way of producing it. – Build your marginal cost curve. – Use price and marginal cost to find the profit- maximizing quantity. – “Find the lowest isocost” • Consumer Problem: – For a given income, find the highest utility you can attain. – “Find the highest indifference curve” Example Indifference Curve 16 1, 16 pf = 16 14 ph = 16 I = 160 12 Football tickets 10 8 6 5, 5 4 4, 4 2 16, 1 0 0 2 4 6 8 10 12 14 16 Hockey tickets Example Indifference Curve 16 pf = 16 14 ph = 16 I = 160 12 Football tickets 10 8 6 5, 5 4 2 0 0 2 4 6 8 10 12 14 16 Hockey tickets Why not (4,4)? Indifference Curve 16 1, 16 pf = 16 14 ph = 16 I = 160 12 Football tickets 10 8 6 5, 5 4 4, 4 2 16, 1 0 0 2 4 6 8 10 12 14 16 Hockey tickets Why not (6,6)? Indifference Curve 16 pf = 16 14 ph = 16 I = 160 12 Football tickets 10 8 6 5, 5 4 2 0 0 2 4 6 8 10 12 14 16 Hockey tickets Demand Indifference Curve 16 pf = 16 14 ph = 16 I = 100 12 Football tickets 10 At a price of 16 (when 8 income is 160 and the price of football tickets 6 5, 5 is 16), you demand 5 4 hockey tickets. 2 0 0 2 4 6 8 10 12 14 16 Hockey tickets Demand Indifference Curve 16 1, 16 pf = 16 14 ph = 16 I = 160 12 Football tickets 10 8 6 5, 5 4 4, 4 2 16, 1 0 0 2 4 6 8 10 12 14 16 Hockey tickets Demand Indifference Curve pf = 16 ph = 16 16 1, 16 14 I = 160 12 Football tickets 10 8 6 5, 5 4 4, 4 2 16, 1 0 0 2 4 6 8 10 12 14 16 Hockey tickets P 16 5 Q Demand Indifference Curve pf = 16 ph = 10 16 1, 16 14 I = 160 12 Football tickets 10 8 6 5, 5 4 4, 4 2 16, 1 0 0 2 4 6 8 10 12 14 16 Hockey tickets P 16 10 5 7 Q Demand Indifference Curve pf = 16 ph = 40 16 1, 16 14 I = 160 12 Football tickets 10 8 6 5, 5 4 4, 4 2 16, 1 0 0 2 4 6 8 10 12 14 16 Hockey tickets P 40 16 10 2 5 7 Q Demand Indifference Curve 16 1, 16 14 12 Football tickets 10 8 6 5, 5 4 4, 4 2 16, 1 0 0 2 4 6 8 10 12 14 16 Hockey tickets P 40 16 10 D 2 5 7 Q Demand p1 = 3 p2 = 3 I = 54 x2 x1 P Q Questions you have to ask • Given these prices and income, what is the most I could buy of each good. • Use these to plot your intercepts • Think about the slope (ratio of prices) Demand p1 = 3 p2 = 3 I = 54 x2 18 18 x1 P 3 9 Q Demand p1 = 4 p2 = 3 I = 54 x2 x1 P 3 9 Q Demand p1 = 4 p2 = 3 I = 54 x2 18 13.5 x1 P 4 D 3 9 Q Demand p1 = 2 p2 = 3 I = 54 x2 x1 P 2 3 9 20 Q Demand p1 = 2 p2 = 3 I = 54 x2 18 27 x1 P 2 3 9 20 Q Demand p2 = 3 I = 54 x2 x1 P 4 3 2 D 3 9 20 Q Demand x2 PERSON 1 x1 Demand x2 PERSON 1 x1 x2 PERSON 2 x1 Demand (Person 2) p1 = 3 p2 = 3 I = 54 x2 18 18 x1 P 4 9 Q Demand p1 = 4 p2 = 3 I = 54 x2 18 13.5 x1 P 4 7 Q Demand p1 = 2 p2 = 3 I = 54 x2 18 x127 P 2 12 Q Demand p2 = 3 I = 54 x2 x1 P 4 3 2 D 7 9 12 Q Demand p2 = 3 I = 54 x2 x2 x1 x1 P P 4 4 3 3 2 2 D D 3 9 20 7 9 12 Q Q Measuring responsiveness • One method is to just look at the slope – When P changes by 1, how much does Q change? – Depends on the scale. – How do you compare TV’s with peaches? • Better method is to use the elasticity – When P changes by 1%, how much (by what percent) does Q change? – Doesn’t depend on scale – Ties directly to revenue/expenditure. Calculating Elasticity • Own-price elasticity %Qx x %Px Calculating Elasticity • Own-price elasticity %Qx x %Px • In this class, you will calculate the arc elasticity: Qx % Qx Ave( Qx ) x % Px Px Ave( Px ) Own price elasticity • Another way to calculate the elasticity is using the point elasticity: 1 Px x slope Qx • Although we won’t use it in this class, it is handy to show some properties of elasticity. Own price elasticity • Own price demand elasticity is (almost) always negative. 1 Px x slope Qx • Why? Own price elasticity • Own price demand elasticity is (almost) always negative. 1 Px x slope Qx • Why? • For this reason, we drop the negative sign. Own price elasticity • Elasticity changes as P and Q change. 1 Px x • Why? slope Qx Own price elasticity • If > 1, say good is elastic at that price 1 Px x • Why? slope Qx Own price elasticity • If < 1, say good is inelastic at that price 1 Px x • Why? slope Qx Own price elasticity • At P=0, elasticity equals 0 1 Px x • Why? slope Qx Own price elasticity • At Q=0, elasticity equals infinity. 1 Px x • Why? slope Qx Own price elasticity • One demand curve may be steeper, but not more inelastic. 1 Px x slope Qx • Why? Example: Demand A: p=10, q=10, slope=-1 Demand B: p=10, q=20, slope=-.5 Own price elasticity At a price of 10, these demand curves have the same elasticity P=10 10 20 P P 4 4 3 3 2 2 D D 3 9 20 7 9 12 Q Q Qx % Qx Ave( Qx ) x % Px Px Ave( Px ) Review • Own price demand elasticity is (almost) always negative (so we ignore the negative). • Elasticity changes as P and Q change! – If > 1, say good is elastic at that price – If < 1, say good is inelastic at that price • At P=0, elasticity equals 0 • At Q=0, elasticity equals infinity. • One demand curve may be steeper, but not more inelastic. • A change in own price is movement along a demand curve (demand is the same, but quantity demand changes).