Let the market demand for rye bread be given by Q = 500 plus I minus 250Prye plu
ID: 1230271 • Letter: L
Question
Let the market demand for rye bread be given by Q = 500 plus I minus 250Prye plus 400Pwheat, where Q is monthly demand in number of loaves, I is average monthly income in dollars, Prye is the price of a loaf of rye bread, and Pwheat is the price of a loaf of wheat bread. If I = $1,000, Prye = $2, and Pwheat = $3, calculate the following (based on 10% changes in denominators):(a) the arc price elasticity of demand for rye bread ?r;
(Hint: assume 10% change makes the price of rye bread rise from $2 to $2.2. Plug $2.2 into equation, you will get Q2)
(b) the arc cross-price elasticity of demand for rye bread Erw;
(Hint: now assume 10% change makes the price of wheat bread rise from $3 to $3.3)
(c) From part (b), are rye bread and wheat bread substitute or complements?
Explanation / Answer
Q=500+ I - 250*Prye +400*Pwheat I= $1000, Prye1 = $2, PWheat1 = $3 So Q1 = 500+1000-250*2+400*3 = 500+1000-500+1200 = 2200 Qrye1 = 250*2 = 500 Qwheat1 = 400*3 = 1200 Now Arc Elasticity of demand EoD = %change in QTy/%change in price As dnominator is inceased by 10%, new value of Prye2 = $2*1.1 = $2.2 & Pwheat2 = $3*1.10 = $3.3 Putting values, we get Qrye2 = 250*2.2 = 550 Qwheat2 = 400*3.3 = 1320 So EoDrye = [(Qrye2-Qrye1)*(Prye2+Prye1)]/[(Qrye2+Qrye1)*(Prye2-Prye1)] ie EoDrye = [(550-500)*(2.2+2)]/[(550+500)*(2.2-2)] = 50*4.2/(1050*0.2) = 210/210 = 1 So Arc elasticity of Rye = 1......Ans (a) EoDwheat = [(Qwheat2-Qwheate1)*(Pwheat2+Pwheat1)]/[(Qwheat2+Qwheate1)*(Pwheat2-Pwheat1)] ie EoDwheat = [(1320-1200)*(3.3+3)]/[(1320+1200)*(3.3-3)] = 120*6.3/(2520*0.3) = 756/756 = 1 So Arc elasticity of Wheat = 1......Ans (b) Thus Rye & wheat are said to have unitary elasticity and small change in their price will not affect total revenue. B. 400 x 3/2,300=0.5217 C. These goods are substitutes Hope this helps
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