Q s =89830-40P s+ 20P x +15P y +2I+0.001A+10W Where Q s=quantity purchased P s=

Question

Qs=89830-40Ps+20Px+15Py+2I+0.001A+10W

Where Qs=quantity purchased

                   Ps= the price of Smooth Sailing sailboats

                   Px= the price of company X’s sailboat

                   Py= the price of company’s Y’s motorboat

                   I= per capita income in dollars

                   A= dollars spent on advertising

                  W=number of favorable days of weather in the southern region of the United States

1.  Characterize this function by circling all in the following list that are applicable:

univariate, bivariate, multivariate, linear, exponential, logarithmic, curvilinear, 1stdegree, 2nddegree, 3rd    degree, additive, multiplicative, linearly homogeneous

2.  What is the numerical value of the partial derivative of the function with respect to the price of Company Y’s motorboats  (be sure to also include the + or – sign)

3.  Write the mathematical symbol representing the coefficient of the number of favorable weather days.  (the numerical value of this coefficient is +10, but the answer you give is to be the symbol representing this partial derivative).

4.  Assuming there is a 1 day increase in the number of favorable weather days, what change in demand for Smooth Sailing’s sailboats will result (give the numerical value of it too)?

5. Are X’s sailboats a substitute for or complementary to Smooth Sailing sailboats?  What feature of the function tells you?  

6.  Are Y’s motorboats a substitute for or complementary to Smooth Sailing sailboats?  What feature of the function tells you?

7.  Are Smooth Sailing sailboats a normal or an inferior good? What feature of the function tells you?

8.  Assuming the price of Y’s motorboats increases by $100, what change in demand for Smooth Sailing’s sailboats will result (give the numerical value, too)?

9.  Assuming per capita income increases by $1000, what change in demand for Smooth Sailing’s sailboats will result (give the numerical value of it, too)?

10.  Assuming the price of X’s sailboats decreases by $100, what change in demand for Smooth Sailing’s sailboats will result (give the numerical value of it, too)?

Explanation / Answer

1. multivariate, linear

There are more than 3 variables which affect Quantity purchased. It is linear function because there is no exponential in the given function.

2. dQs/dPy = + 15

3.dQs/dW = + 10

4. Qs = 89830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10W

Qs = 89830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10(W+ 1)

Qs = 89830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10W + 10

Qs' = Qs + 10

Qs increases by 10 units.

5. Qs = + 20Px

Substitute goods because increase in price of X i.e. Px causes increase in Qs.

6. Qs = + 15Py

Substitute goods because increase in Py causes increase in Qs

7. Qs = 2I

Increase in income causes increase in Qs i.e. smooth sailing sailboats is a normal good.

8. Qs = 89830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10W

Qs' = 89830 - 40Ps + 20Px + 15(Py + 100) + 2I + 0.001A + 10W

Qs' = 89830 - 40Ps + 20Px + 15Py + 1500 + 2I + 0.001A + 10W

Qs' = Qs + 1500

Demand increases by 1500 units

9. Qs = 89830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10W

Qs' = 89830 - 40Ps + 20Px + 15Py + 2(I + 1000) + 0.001A + 10W

Qs' = 89830 - 40Ps + 20Px + 15Py + 2I + 2000 + 0.001A + 10W

Qs' = Qs + 2000

Demand increases by 2000 units.

10. Qs = 89830 - 40Ps + 20Px + 15Py + 2I + 0.001A + 10W

Qs' = 89830 - 40Ps + 20(Px - 100) + 15Py + 2I + 0.001A + 10W

Qs' = 89830 - 40Ps + 20Px - 2000 + 15Py + 2I + 0.001A + 10W

Qs' = Qs - 2000

Demand decreases by 2000 units.

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