Question

Your marketing research department provides the following estimated demand function for your product: Qd = 500.6 - 11.4P + 0.5INCOME where P is the price of your product and INCOME is average income.

a. Is your product a normal good or an inferior good? Explain your answer.

b. The standard error for the price coefficient is 2.0. What is its t-statistic? What can you conclude about the coefficient's statistical significance?

c. The standard error for the income coefficient is 0.3. What is its t-statistic? What can you conclude about the coefficient's statistical significance?

Answer 1

a) A product is called a normal good for which when income increases, the quantity demanded also increases. For inferior goods, an increase in income is attached with a decrease in the quantity demanded. Here, we can clearly see that -

Thus, the product is a normal good.

Consider t-stat,

b) H₀ : Price coefficient equals 0 vs H₁ : Price coefficient is significantly different from 0

test statistic, t_calc1 = = -5.7 is the required t-statistic.

-5.7 is a large value such that it is safe to say that the test statistic lies in the rejection region such that . Thus we have sufficient evidence to reject the null hypothesis. [note: we can't find exact figures since 'n' is not given but above t-stat gives the result accurately]

c)  H₀ : Income coefficient equals 0 vs H₁ : Income coefficient is significantly different from 0

test statistic, t_calc2 = = 1.67

This is a very small number. Consulting the t-tables, it can be seen that even with infinite number of products, at 10% level of signifcance and two sided test, the value of t is 1.645 < 1.67. At 5%, and infinite 'n'. the limits are +(-)1.96. Considering a 5% LOS to be a better result we can say that the calcuated t statistics lie in the acceptance region. Thus we have sufficient evidence to reject the alternative hypothesis of significance and the income coefficient is insignificant here.

Thank You and Best of Luck