Assume that the Japanese car maker, Toyota has successfully established an assembling plant of cars at Okahandja and its annual production is unknown.  Assume that the demand function for the automobile industry is:

Q = β1P + β2PI + β3I + β4Pop + β5i + β6A                                                                                                                (1)

where Q is the quantity of cars demanded (dependent variable) and is a linear function of all the independent variables; P is the average price of new domestic cars (in N$); PI is the average price for new import cars (in N$); I is disposable income per household (in N$); Pop is population (in millions); i is average interest rate on car loans (in percent); and A is industry advertising expenditures (in N$ millions).

1.  The terms β1, β2, …, β3 are parameters of the demand function. Explain the determinants of quantity of cars demanded as stated in equation 1 and clarify the expected relationship between each parameter and quantity of cars demanded. Motivate the rationale for each of the demand variables in equation 1.                    (10)  
2. Assume that the parameters of the demand function (equation 1) are known with certainty, as shown in the following equation.

Q = –450P + 155PI + 155I + 5,500Pop – 2,500,000i + 100A ……..(2)                                                                           

Using equation 2, explain the effects of the changes in the independent variables on the dependent variable.                                                                                                                                                                          (10)  

3. The information below shows the estimated value for independent variables during the coming year.

 

Independent variable	Estimated value for independent variable
Average price for new cars (P) (N$)	25,000
Average price for new luxury cars (PI) (N$)	55,000
Disposable income, per household (I) (N$)	40,000
Population (Pop) (millions)	350
Average interest rate (i) (percent)	7%
Industry advertising expenditures (A) (N$ million)	5,000

 

4. Calculate the total demand (millions of cars)