Name

$(8)$ Due

Please show work in detail.

All questions utilize the multivariate demand function for Toyotas given in C $4$ on text page $82,$ initially with:

Initial values are: $,P_M=$$$20000,P_G=$$$1\mathrm{.}00,I=$$$15000,A=$$$10000$

This function is: $,Q_T=200-\mathrm{.}01P_T+\mathrm{.}005P_M-10P_G+\mathrm{.}01I+\mathrm{.}003A$

$1.($a$).$ Use the above to calculate the arc price elasticity of demand between $P_T=$$$20000$ decreasing to $P_T=$$$10000.$ The arc elasticity formula is: $E_p=\frac{Q}{P}*\frac{P_1+P_2}{Q_1+Q_2}$

$($b$).$ Judging from the computation in $(1$a$),$ do you expect the revenue resulting from the price decrease to $$10000$ to increase, remain the same, or decrease relative to the revenue at the price of $$20000?($Hint: see the table on page $65$ of Truett$).$ Explain

your choice.

$2.($a$)$ Calculate the point price elasticity of demand for Toyotas at $P_T=$$$20000($which should make $Q_T=270).$ Other variables and their values are given at the top, before question #$1.$ The formula is:

$E_P=\frac{del{Q}_T}{del{P}_T}*\frac{P_T}{Q_T}$

$($b$).$ Does this elasticity indicate that Toyota demand is relatively responsive to changes in Toyota price? Explain why or why not.

$3.($a$).$ Calculate the point gasoline cross$-$price elasticity between $(P_G)$ and Toyota demand $(Q_T).$ Assume the price of gasoline is $P_G=$$$1\mathrm{.}00.$ Use $P_T=20000($which should make $Q_T=270).$ Other variables and their values are given at the top, before

question #$1.$ The formula is:

$E_{TG}=\frac{del{Q}_T}{del{P}_G}*\frac{P_G}{Q_T}$

$($b$).$ 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.

$4.($a$).$ Competition might be a worry for Toyota. $P_M=$ the price of Mazadas. Calculate the point Mazada cross$-$price elasticity of demand with $P_M=$$$20000$ and $P_T=$$$20000$

$($which should make $Q_T=270).$ Other variables are given at the top before

question #$1.$ The formula is:

$E_{TM}=\frac{del{Q}_T}{\text{d}\text{e}\text{l}\text{P}\text{m}}*\frac{Pm}{Q_T}$

$($b$).$ Does this elasticity indicate that the demand for Toyotas is relatively responsive to changes in the price of Mazadas? Explain why or why not.

$5.($a$).$ Calculate the point advertising elasticity of demand for advertising expenditures $(A)=$$$10000$ also with $P_T=$$$10000($which should make $Q_T=370).$ Other variables and their values are given at the top, before question #$1.$ The formula is:

$E_A=\frac{del{Q}_T}{\text{d}\text{e}\text{l}\text{A}}*\frac{A}{Q_T}$

$($b$).$ Does this elasticity indicate that demand for Toyotas is very responsive to changes in advertising expenditures $($thus suggesting that advertising is a very important way to increase sales$)?$ Explain why or why not.