Question

You are managing a division of a large company. The marketing department submits a report to you about the demand for the product you manage. The report includes the following estimated demand​ function: Qd =2,910.0 -11.3 P + 0.050 INCOME- 3.0

(100.4​)    ​(3.2​)   ​(0.012​)               ​(1.0​)

where P is the price of your​ product, INCOME is average​ income, Upper P Subscript other is the price of a related​ product, and the numbers in parentheses are the standard errors of the estimated coefficients directly above them. The Upper R squared statistic for the regression is 0.84​ (84 percent).

Which of the following comments about the estimated demand function are​ true? ​(Check all that apply.​) A. It would be useful for forecasting the demand of the product as the Upper R squared statistic for the regression is high. B. It would not be useful for forecasting the demand of the product as the estimated coefficients are not statistically significant. C. It would be useful for forecasting the demand of the product as the estimated coefficients are statistically significant. D. It would not be useful for forecasting the demand of the product as the Upper R squared statistic for the regression is low.

The product is a _____good. The related product is a complement for your product because​

A. the estimated coefficient for income is positive and statistically significant B. the estimated coefficient for price of the good is negative and statistically significant C. the estimated coefficient for the intercept is positive and statistically significant D. the estimated coefficient for price of the related good is negative and statistically significant

Suppose the current price of your product is ​$180​, average income is ​$55​, and the price of the related product is ​$300. The quantity demanded will be _______. Based on the given information and your calculations in the previous​ step, the price elasticity of demand for your product will be _____ ​(Round your answer to three decimal places.​) If you raise the price of your​ product, the total revenue will ______.

Answer 1

Solution:

We have:

Qd = 2910.0 - 11.3*P + 0.050*INCOME - 3.0*Pother ... (*)

t-value = estimated coeff/std error

See that for each parameter, the t-values are very high (greater than 3) and as a rule of thumb, it means that the variables are then statistically significant. Also, the R^2 is very high, indicating that model is a good fit. So, both these indicate that the found out regression result is suitable for forecasting. So, correct options are (A) and (C).

Notice that the coefficient of income = +0.05, which is positive. In other words, the demand function indicates that there is a positive relation between income of the consumer and his/her demand for the given product. Since, increase in income increases the demand for the product, this product is a normal good.

The two goods are complements when they are consumed together. This means that if price of a related good increases, the demand for that related good will decrease (law of demand); further since the two goods are consumed together, it means demand for the other good will also decrease. So, clearly if the two goods are complements, there exists a negative relation between price of one good and demand for other good. Since, the coefficient of price of other related good = -3.0, which is negative (indicating a negative relation between price of related good and the good/product in question) and also statistically significant (|coeff/std error| = |-3/1| = 3 (the t-value of 3 is very high). So, the correct option is (D) the estimated coefficient for price of related good is negative and statistically significant.

We are given the following information:

P = $180, INCOME = $55, Pother = $300, so using (*), we have

Qd = 2910.0 - 11.3*180 + 0.050*55 - 3.0*300

Qd = 2910.0 - 2034 + 2.75 - 900 = -21.25

Since, demand is always non-negative, for the given values, quantity demanded will be 0.

Price elasticity of demand, ed = (dQ/dP)*(P/Qd)

Since we found Qd to be 0 for above values, ed = infinity (perfectly inelastic)

Notice that even at given price, demand is 0, so increasing the price any further will still result in 0 quantity demanded and so the total revenue will be 0.

**Please recheck the values you've provided in the question, and check for any typos, as otherwise the answers will be altered.