Question

A company produces a brand of yoghurt for which the following two demand equations have been estimated.

            (i) Q = 3.6     -      0.2P_y     –    0.6I      +     0.7P_i

                        (2.75)       (-2.87)         (-2.54)         (3.71)

            Number of observations = 60, R² = 0.96 (numbers in brackets are t-statistics)

            (ii) Q = 2.4   -    0.5P_y    +    0.8I     –    0.4P_i

                        (1.15)    (2.01)         (2.11)       (-1.67)

            Number of observations = 60, R² = 0.68 (numbers in brackets are t-statistics)

Where Q = number of units of yoghurt demanded, P_y = price of yoghurt, I = disposable income, and P_i = ice cream.

1. Which equation would you recommend and for what reason? Please explain.
2. Each equation tells you something about the relationship between yoghurt and ice-cream. What is the difference between the two relationships described by the two equations? Please give an explanation.
3. What is the difference in the relationship between yoghurt and income between the two equations? Please give an explanation.

Answer 1

a.

The recommended equation is Q = 3.6     -      0.2P_y     –    0.6I      +     0.7P_i (Equation (i)), because R² = 0.96 of the equation (i) is greater than that of equation (ii)

b.

The coefficient of ice-cream in equation (i) is positive.

The coefficient of ice-cream in equation (ii) is negative.

Equation (i) suggests that there is a positive relation between demand of yoghurt and ice-cream. That is, the demand of yoghurt increases as the price of  ice cream increases and vice-versa.

Equation (ii) suggests that there is a negative relation between demand of yoghurt and ice-cream. That is, the demand of yoghurt decreases as the price of  ice cream increases and vice-versa.

c.

The coefficient of income in equation (i) is negative.

The coefficient of income in equation (ii) is positive.

Equation (i) suggests that there is a negative relation between demand of yoghurt and income. That is, the demand of yoghurt decreases as the income increases and vice-versa.

Equation (ii) suggests that there is a positive relation between demand of yoghurt and income. That is, the demand of yoghurt increases as the income increases and vice-versa.