Toyota estimates that demand for its 2003 Toyota Corolla will depend on the price they charge (P), the interest rate that they offer consumers to finance a car (i),and the growth rate of disposable income (D). Months of historical data have led to the estimation of the following demand relationship: Q=578-28P-5i+30Dwhere Q is the number of cars sold in a month (in thousands), P is the price of the car (in thousands), i is the interest rate charged to finance car sales (expressed as a percentage, i.e. i=10 represents 10%) and D is the growth rate of disposable income (expressed as a percentage, i.e. D=2 represents 2%). The projected values of these variables for October 2003 are P=17, i=10, and D=2.

a.What are the projected sales of Corollas in October, 2003?

b.Toyota is contemplating a sales campaign that would either lower the price of the car or cut interest rates for car purchases. What would be the impact on October, 2003 car sales of a $500 price cut (P falls by 0.5)? What would be the impact on October, 2003 car sales of 0% financing (assume the price stays at 17)? Which campaign would you choose? Explain.

c.If the marginal cost of producing a Toyota Corolla is 12 (marginal cost is also expressed in thousands, so MC=12 indicates a marginal cost of $12,000 per car), what is the profit maximizing price?

d.How much would you have to change the interest rate to sell the profit maximizing quantity of Corollas computed in part c (assuming that the price remains at $17,000-i.e. P=17)?

e.Further research by Toyota into the demand for its Corolla model indicates that there are two distinct groups of customers. One group is more sensitive to interest rates and the other group is more sensitive to prices. Toyota is able to distinguish the two groups based on whether they are looking to obtain financing from Toyota or whether they come to the showroom with their own financing. Statistical analysis indicates that the two groups have the following demand curves: Q1=300-12P1-3i+15DQ2=278-16P2-2i+15DAssuming that i=10 and D=2, what price should Toyota charge to the two groups of customers? How many cars will they sell to each group? How much higher will profits be compared to the single profit maximizing price computed in part c?