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Given the demand function Q = 24 – 1.5P 1. Calculate the point price elasticity at a price of $14 EP = (ΔQ/ΔP) *(P/Q) = (-1.5) *(14/3) = (-1.5) *(4.667) = -7.001 2. Calculate the point price elasticity at a price of $8 EP = (Δ Q/ Δ P) *(P/Q) = (-1.5) *(8/12) = (-1.5) *(.667) = -1 3. Calculate the point price elasticity at a price of $5 EP = (Δ Q/ Δ P) *(P/Q) = (-1.5) *(5/16.5) = (-1.5) *(.303) = -.455 An application of price elasticity of demand. If the quantity demanded for milk were 100 units and the price elasticity of demand for milk was -.6 If the price of milk increased by 8%, how much would the quantity demanded change? EP= (%Δ Q/ %Δ P) -0.6= (%Δ Q%/8), so solving for %Δ Q, %Δ Q= (8%) (-.6) = - 4.8% An 8% increase in price will reduce the quantity demanded by 4.8% Assume in the market for coffee at p=$4.5, Qd=4 cups; when price decreased to $3.00, Qd changed to 6 cups. Using the midpoint method, what is the price elasticity of demand for coffee. %Δ Price=100*[($3.00- $4.50)/($4.5+$3)/2] %Δ Price= -40% %Δ Quantity=100*[(6-4)/(6+4)/2] %Δ Quantity=40% EP= (%Δ Q/ %Δ P) = 40%/-40% EP=-1, 1 in absolute value, Coffee’s demand is unit elastic. Using the Base Formula, what is the price elasticity of demand for coffee. %Δ Price=100*[($3.00- $4.50)/$4.5] %Δ Price= -33.33% %Δ Quantity=100*[(6-4)/4] %Δ Quantity=50% EP=(%Δ Q/ %Δ P)= 50%/-33.33%= - 1.5 EP=-1.5, 1.5 in absolute value, more than 1, Coffee’s demand is price elastic.

Whereas the own-price elasticity of demand measures the responsiveness of quantity to a goods own price, cross-price elasticity of demand shows us how quantity demand responds to changes in the price of related goods. Whereas before we could ignore positives and negatives with elasticities, with cross-price, sign matters. Our equation is as follows:

A complement will have a negative cross-price elasticity, since if the % change in price is positive, the % change in quantity will be negative and vice-versa. A substitute will have a positive cross-price elasticity, since if the % change in price is positive, the % change in quantity will be positive and vice-versa. Goods can be normal or inferior depending on how a consumer responds to a change in income. This responsiveness can also be measured with elasticity by the income elasticity of demand. Our equation is as follows:

A normal good will have a positive income elasticity, since if the % change in income is positive, the % change in quantity will be positive and vice-versa. A inferior good will have a negative income elasticity, since if the % change in income is positive, the % change in quantity will be negative and vice-versa.

Summary Elasticity is a measure of responsiveness, calculated by the percentage change in one variable divided by the percentage change in another. Both mid-point and point-slope formulas are important for calculating elasticity in different situations. Mid-point gives an average of elasticities between two points, whereas point-slope gives the elasticity at a certain point. These can be calculated with the following formulas:

Base Formula

Mid-Point Formula

Point-Slope Formula...