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 $3.00 (You must first find the market equilibrium price and quantity in order to see how the $3.00 relates to them)?
Q = 100 – 4.6P and Q = XXXXXXXXXX2P
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 = XXXXXXXXXX2P and Q = 80 – 4.6P
3. Circle the function on the answer sheet that represents the marginal revenue (MR) function for this demand function: Q = 150 – 5P
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 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 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: