1.The following two linear functions represent a market (thus one is a supply function, the other a demand function). find the answer closest to being correct.What will suppliers willingly supply if market price is controlled to be $1.50 (You must first find the market equilibrium price and quantity in order to see how the $1.50 relates to them)?Q = 100 - 4.6PandQ = 75 + 6.2P

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

Q = 70 + 6.2PandQ = 100 - 4.6P

3.What is the function that represents the marginal revenue (MR) function for this demand function:Q = 100 - 4.6P

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

5.If supply decreases and demand also decreases, we can conclude that the new equilibrium:

The multivariate demand function (below) is needed for questions 6 - 12.

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 = 65000 - 20Pj + 20Pf + 35Pt - 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A

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 Ford's hybrid (Pf) increases by $500, then the demand for Jolts will:

7.Average weekly Jolt advertising expenditure (A) has increased by $450.The demand for Jolts then should:

8.You can tell by looking at the sign of the price of replacement batteries (Pb) that batteries are:

9.The partial derivative of the demand for Jolts with respect to the price of Toyota hybrids (Pt) 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.Pj = $40000Pf = $35000Pt = $40000Pb = $9000

Tc =$9000Y = $1100Mg = 40A = $20000

11.What is the point price elasticity of demand of Jolts with respect to the Ford price (Pf) of $35000?Work out completely, also show the sign (+ or -), carry out to three decimal places.

12.What is the point elasticity of Jolt demand with respect to the miles per gallon rating (Mg) of 40?Work out completely and show the sign (+ or -), carry out to four decimal places.

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

13.If a 10% increase in the price of gas causes a 25% decrease in demand for standard sized autos, then the cross-price elasticity of demand is:

14.If the price elasticity of demand for gasoline is 1.3,then a 15% increase in quantity demanded is caused by:

15.A 5% increase in the price of 40 inch LCD televisions which have a price elasticity of 1.8 will cause a:

16.A business newscast claims that the median home price of existing homes fell from $315000 to $295000.Over the same time period the quantity of these homes sold fell from 2900000 to 2800000.Using the arc elasticity formula, calculate the arc elasticity implied.

17.The demand for a product is income inelastic with an elasticity coefficient of 0.25.If there is a 30% decrease in demand, what must the decrease in income be?

18.The cross price elasticity of biscotti demand with respect to the price of Lattes is -0.35 (Lattes and biscotti are complementary goods).If the price of Lattes decreases 20%, what would you expect to happen to biscotti demand?

19.Write the first derivative of the following function

Y = 150 -20X² +5X³ -10X +30

20.Write the first derivative of the following function

Y = 15X^1/5 + 10X^4/3 -X^1/2 + 20X -55