Use the above to calculate the are price elasticity of demand between P_T = $200

Question

Use the above to calculate the are price elasticity of demand between P_T = $20000 and P_T = $15000. The are elasticity formula is; E_p = Delta Q/Delta P middot P_1 + P_2/Q_1 + Q_2 Calculate the quantity demanded at each of the above prices and revenue that will result if the quantity is sold (fill in table below) Marketing suggests lowering P_T from $20000 to $15000. The size of the elasticity coefficient in notequalto should tell you what is likely to happen to revenue. Explain why this is (or is not) a good marketing suggestion from a revenue viewpoint Assume the P_T $17500 (which should make Q^T = 295). Now, using the point elasticity formula below, calculate the point price elasticity of demand. Is this point elasticity coefficient the same as the are coefficient in notequalto 1? Why docs this make sense if the two are the same? If the two differ, does this make sense and why? The formula is: E_P = Q_T/P_T middot P_T/Q_T Calculate the point gasoline cross-price elasticity of demand with P_G = $1.00. Use Q_T corresponding to P_T = $20000. Other variables and their values are given at the top, before question notequalto 1. Does this elasticity indicate that the demand for Toyotas is relatively responsive to changes In the price of gasoline (P_G)? Explain why or why not. The formula is: E_CROSS = Q_T/P_G middot P_G/Q_T Competition might be a worry for Toyota Mazdas arc represented by P_M. Calculate the point Mazdas cross-price elasticity of demand with P-M = $20000 and Pr - $20000 Docs this elasticity coefficient indicate that the demand for Toyota, is relatively responsive to changes in the price of Mazdas? Explain why or why not The formula is. E_CROSS = Q_R/P_M middot P_M/Q_R Elasticity 8.doc June 27, 2016

Explanation / Answer

1.

Qt = 200 - .01*Pt + .005Pm – 10Pg +.01I +.003A ----------------------- (1)

Differentiation of equation 1 w.r.t. Pt

dQt/dPt = -.01

Also,

At Pt = $20000

Qt = 200 - .01*20000 + .005*20000 – 10*1 +.01*15000 +.003*10000 = 270

At Pt = $15000

Qt = 200 - .01*15000 + .005*20000 – 10*1 +.01*15000 +.003*10000 = 320

Now, as per the given formula,

E = (dQt/dPt)*((P1+P2)/(Q1+Q2))

E = (-.01)*((15000+20000)/(320 + 270))

E = -.593

2.

At Pt = $20000

Qt = 200 - .01*20000 + .005*20000 – 10*1 +.01*15000 +.003*10000 = 270

Revenue = 270*20000 = $5400000

At Pt = $15000

Qt = 200 - .01*15000 + .005*20000 – 10*1 +.01*15000 +.003*10000 = 320

Revenue = 320*15000 = $4800000

3.

Percentage change in price in Q. 2= (15000 – 20000)/20000 = - 25%

Percentage change in revenue in Q. 2 = (4800000 – 5400000)/5400000 = -11.11%

Percentage change in Quantity in Q. 2 = (320 – 270)/270 = 18.51%

Elasticity calculated in Q.1 is -.59. it is less than 1 and it means that demand is relatively less responsive (Relative inelastic) to the change in price. it is confirmed by the answers in Q.2.

When, price is decreased by 25%, demand of quantity only increases by 18.51%. it causes into the loss of revenue of 11.11%. thus, elasticity can be considered as a measure when a pricing decision takes place as a part of marketing strategy.

Thus, answers in Q2 is backed by the elasticity calculated in Q.1.

4.

Ep = (-.01)*(17500/295) = -.593

Elasticity of Q.4 is as same as elasticity of Q1 because it is coming through the expression that has included all the factors that affect the demand with the change in price.

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