PM = $20000 PG = $1.00 I = $15000 A = $10000
This function is:
QT = 200 -.01PT +.005PM -10PG +.01I +.003A
1. Use the above to calculate the arc price elasticity of demand between PT = $20000 and PT = $15000. The arc elasticity formula is:
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).
| PT | QT | Revenue |
| $20000 | | |
| $15000 | | |
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 Mazda 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: