Question

Application of demand and supply theory

Question 1

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)                                                                  (5)  

Answer 1

Answer)

In eq(1) , we are given the following parameter:

(i) P -> It denotes the average price of the new car and has negative coeffic8ent meaning that as the new car price increases, the demand decreases.

(ii) PI -> As, the price of new luxury cars increases, the demand for new cars increases as the luxury cars and new cars are substitute goods for each other.

(iii) I -> As, the income of an individual increaes the demand for new cars also increases and thus there is a positive relationship between the income and demand for new cars.

(iv) Population -> As, the population increases , more people wish to buy tue car and this the demand for new cars increases.

(v) i -> As, the interest rate increases, the demamd for new cars decreases and thus there is a negative relationship between the demamd for new cars and interest rates.

(vi) A -> As, the advertisement expenditure increases, the demand for new cars increases.

As, we are given the econometric equation as follows:

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

As, we are also given the estimated value of each parameter, so, we substitute those values in the equation above as follows:

Q = -450(25000) + 155(55000) + 155(4000) + 5500(350) - 2,500,000(0.07) + 100(500)

On calculating the equation above , we get the demqnd as follows:

Q = 5,725,000 (millions)