Question

(PLEASE)

The XYZ marketing firm found that a particular brand of portable stereo has the following demand curve: Q = 10,000 – 201P + 0.029 Pop. + 0.61 I + 0.22 A
Where Q is the quantity demanded per month, P is the price ($), Pop. is population (in units), I is income ($), and A is advertising expenditures ($).
a. Are the signs of the individual coefficients consistent with predictions from economics theory? Concisely explain. (4pts) b. Interpret the effect of each explanatory variable on Q. (4pts) c. Determine the demand function for the company in which P = 300, Pop. = 1,000,000, I = 30,000, A = 15,000. (4pts) d. Calculate the price necessary to sell 45,000 stereos. (1pts) e. If income decreases by $10,000, in which direction and by how much should advertising expenditures change to cancel out this change in income? (5pts)

Answer 1

A.

Yes, signs of the coefficients are consistent with the economics theory, as increase in price leads to decrease in quantity, shown with negative signs, increase in population, income and advertising expenditure to increase the demand in quantity, so given by the positive sign. Hence, signs of the coefficients are consistent with what economics suggests.

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B.

Q = 10000 – 201P + 0.029 Pop. + 0.61 I + 0.22 A

As per the above equation,

With one unit of increase in price, there is a decrease in 201 units in quantity demanded and vice versa.

With one unit of increase in population, there is an increase in 0.029 units in demand of the quantity and vice versa.

With one unit of increase in income , there is an increase in 0.61 units in demand of the quantity and vice versa.

With one unit of increase in Adv. Exp., there is an increase in 0.22 units in demand of the quantity and vice versa.

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C.

With the given data,

Q = 10000 - 201*300 + 0.029*1000000 + 0.61*30000 + 0.22*15000

Q = 300 units

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D.

If Q = 45000

Then,

45000 = 10000 - 201*P + 0.029*1000000 + 0.61*30000 + 0.22*15000

10000 - 201*P = (45000 - (0.029*1000000 + 0.61*30000 + 0.22*15000))

P = (10000 - (45000 - (0.029*1000000 + 0.61*30000 + 0.22*15000)))/201

P = 77.61

So, price should be 77.61.

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E.

As per the changed scenario, income = 20000 now,

Let, Q = 300 as same as before the decrease the income, then:

300 = 10000 - 201*300 + 0.029*1000000 + 0.61*20000 + 0.22*A

A = (300 - 10000 + 201*300 - 0.029*1000000 - 0.61*20000)/.22

A = 42727.27

Increase in advertising expenditure = 42727.27 - 15000

Increase in advertising expenditure = $27727.27

Hence, advertising expenditure will increase positively and in the magnitude of $27727.27.