Qt=200-0.01Pt+0.005Pm-10Pg+0.01I+0.003A Qt= quantity purchased Pt= the average p
ID: 1225840 • Letter: Q
Question
Qt=200-0.01Pt+0.005Pm-10Pg+0.01I+0.003A
Qt= quantity purchased
Pt= the average price of Toyotas Pm=the average price of mazdas
Pg=the price of gasoline I=per capita income A=dollars spent annually on advertising
3. Marketing suggests lowering PT from $20000 to $15000. The size of the elasticity coefficient in #1 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 (note: your answer in #1 and the calculations in #2 should be giving the same message). If the implications in #1 and #2 differ, does the difference make sense (or did you make a mistake in #1 or #2)?
4. Assume the PT = $17500 (which should make QT = 295). Now, using the point elasticity formula below, calculate the point price elasticity of demand. Is this point elasticity coefficient the same as the arc coefficient in #1? Why does this make sense if the two are the same? If the two differ, does this make sense and why? The formula is:
5. Calculate the point gasoline cross-price elasticity of demand with PG = $1.00. Use QT corresponding to PT = $20000. Other variables and their values are given at the top, before question #1. Does this elasticity indicate that the demand for Toyotas is relatively responsive to changes in the price of gasoline (PG)? Explain why or why not. The formula is:
6. Competition might be a worry for Toyota. Mazdas are represented by PM . Calculate the point Masda cross-price elasticity of demand with PM = $20000 and PT = $20000. Does this elasticity coefficient indicate that the demand for Toyotas is relatively responsive to changes in the price of Mazdas? Explain why or why not. The formula is:
Explanation / Answer
Qt=200-0.01Pt+0.005Pm-10Pg+0.01I+0.003A
3) We know that when price was 20,000 quantity demanded was 270 and if price drops to 15,000 quantity demand would be 320.
The elasticity that was measured in previous part is supposed to be -0.59.
As the elasticity is below 1, if we take absolute value only, it signifies that with change of price there would be no significant effect on demand. This means that if prices decreases, the proportionate increase in demand will be less than proportionate decrease in price. thus decreasing price is not good suggestion.
Secondly when TR measured in previous part, we found that TR when price was 20,000 was 54,00,000 and when price reduces TR reduces too , it becomes 48,00,000. Thus decreasing good gives less revenue and hence less profit. Thus it is not a good decision.
4) Point elasticity is find out by differentiating demand function with respect to p and multiplying with ratio of price and quantity.
that is point elasticity = dQ/dP = P/Q
elasticity = -0.01 * (17500/295) = -0.593
The point elasticity is same as arc elasticity.
Obviously these two elasticities have different method but measure same thing with same parameters hence elasticities are same.
5) cross elasticity of gasoline = dQ/dPg * (Pg/Q)
when Pt = 20,000 Q = 270 and Pg = 1.
cross elasticity = -10 (1/270) = -0.037.
This elasticity is less than 1 (absolute value) it implies that the demand for Toyotas is not relatively responsive to changes in the price of gasoline.
6) Cross price elasticity = dQ/dPM * (PM/Q)
when Pt = 20,000 Q = 270 and PM = 20,000.
Cross price elasticity = 0.005 * (20000/270) = 0.37
Again This elasticity is less than 1 (absolute value) it implies that the demand for Toyotas is not relatively responsive to changes in the price of Mazdas.