$1.$ The following two linear functions represent a market $($thus one is a supply function, the other a demand function$).$ Circle the answer closest to being correct. Approximately what will the quantity demanded be if the government controls the market price to be $$3\mathrm{.}00($You must first find the market equilibrium price and quantity in order to see how the $$3\mathrm{.}00$ relates to them$)?$

Q $=1004\mathrm{.}6$P and Q $=75+6\mathrm{.}2$P

$2.$ There has been a change in the market $($represented in $1$ above$).$ The change is represented by the following two equations. Circle the one correct conclusion that describes the market change.

Q $=65+6\mathrm{.}2$P and Q $=804\mathrm{.}6$P

$3.$ Circle the function on the answer sheet that represents the marginal revenue $($MR$)$ function for this demand function: Q $=1505$P

$4.$ Circle the quantity that maximizes total revenue $($TR$)$ for the marginal revenue $($MR$)$ function selected in number three $(3).$

$5.$ If supply remains unchanged but demand increases, we can conclude that the new equilibrium:

The multivariate demand function $($below$)$ is needed for questions $612.$

Setting: U$.$S$.$ Auto manufacturers are trying to develop a multivariate function with which to estimate the demand for their gas$-$electric hybrid compact cars. Here is one that Motors General developed for its Jolt:

Qj $=6500020$Pj $+20$Pf $+35$Pt $5$Pb $+0\mathrm{.}2$Tc $+0\mathrm{.}05$Y $+10$Mg $+0\mathrm{.}04$A

Where

Qj $=$ the number of Jolts demanded per week.

Pj $=$ the price of each new Jolt $($in $$).$

Pf $=$ the price of each new Ford gas$-$electric hybrid $($in $$).$

Pt $=$ the price of each new Toyota gas$-$electric hybrid $($in $$).$

Pb $=$ the price of replacement batteries for the Jolt $($in $$).$

Tc $=$ the amount of tax credit incentive offered with the purchase of a new hybrid $($in $$).$

Y $=$ average weekly disposable income of a typical Jolt purchaser $($in $$).$

Mg $=$ the miles per gallon of gas rating of the Jolt $($in miles per gallon$).$

A $=$ average weekly Jolt advertising expenditure $($in $$).$

$6.$ If all variables remain unchanged except that the price of the Toyota hybrid $($Pt$)$ decreases by $$500,$ then the demand for Jolts will:

$7.$ Engineering increases the miles per gallon of gas rating $($Mg$)$ by $10$ miles per gallon. The manager of the advertising department should point out that demand for Jolts will:

$8.$ You can tell by looking at the sign Ford hybrids $($Pf$)$ that Ford hybrids are being considered:

$9.$ The partial derivative of the demand for Jolts with respect to advertising $($A$)$ is:

$10.$ Enter the following values into your Jolt demand function $($be very careful with the calculation because the resulting quantity of Jolts demanded will be used in several questions to follow$).$ Circle your answer on the answer sheet. Pj $=$ $$30000$ Pf $=$ $$45000$ Pt $=$ $$55000$ Pb $=$ $$6000$

Tc $=$ $$10000$ Y $=$ $$1500$ Mg $=60$ A $=$$$50000$

$11.$ What is the point cross$-$price elasticity of Jolt demand with respect to the Toyota price $($Pt$)$ of $$55000?$ Work out completely and show the sign $(+$ or $-)$; carry out to $3$ decimal places. The formula is:

$12.$ What is the point elasticity of Jolt demand with respect to the advertising expenditure $($A$)$ of $$50000.$ Work out completely and show the sign $(+$ or $-)$; carry out to four decimal places. The formula is:

Answers to the following problems do not depend on any information from above.

$13.$ If a $10\%$ decrease in the price of gas causes a $30\%$ increase in the demand for standard sized autos, then the cross$-$price elasticity of demand is:

$14.$ If the price elasticity of demand of for gasoline is $1\mathrm{.}8,$ then a $15\%$ decrease in quantity demanded is caused by a:

$15.$ A $10\%$ increase in the price of $40$ inch LCD televisions which have a price elasticity of demand of $2\mathrm{.}5$ will cause a:

$16.$ A business newscast claims that the median home price of existing homes fell from $$450000$ to $$350000.$ Over the same time period the quantity of these homes sold fell from $4100000$ to $3900000.$ Using an arc elasticity formula, calculate the arc elasticity implied. The formula is:

$17.$ The demand for a product is income elastic with an elasticity coefficient of $2\mathrm{.}00.$ If there is a $35\%$ increase in income then what will the increase in demand be$?$

$18.$ The cross$-$price elasticity of biscotti demand with respect to the price of Lattes is $-2\mathrm{.}20($Lattes and biscotti are complementary goods$).$ If the price of Lattes increases $20\%$ what would you expect the demand for biscotti to be$?$

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$19.$ Write the first derivative of the following function in the space on the answer sheet.

Y $=15-4$X$2+6$X$3$

$20.$ Write the f

irst derivative of the following function in the space on the answer sheet.

Y $=6$X$3/22$X$1/2+3$X$4-100$