Question

Analyze the demand function for Cuisine Tech Inc.’s (CTI) deluxe microwave ovens given on page 170. Please also read “What is a Symbol” located in the folder with this assignment.

This function is:

                        Q_H = 60000 -40P_H + 20P_C + 5H + .1I_H + .0001A_H

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

            univariate, bivariate, multivariate, linear, exponential, logarithmic, curvilinear, 1^st degree, 2^nd degree, 3^rd     degree, additive, multiplicative, linearly homogeneous

2. What is the numerical value of the partial derivative of the function with respect to average annual income (I_H) (be sure to also include the + or – sign. Note: I do not want the symbol for this partial derivative)?

3. Write the mathematical symbol representing the coefficient of the number of two-income households. (H, the numerical value of this coefficient is +5 [which represents 5 million two-income households], but the answer you give is to be the symbol representing this partial derivative).

4. Assuming the number of two-income households (H, in millions) employed increases by one, what change in demand for CTI ovens will result (give the numerical value of it, too)?

5. Are CTI ovens a normal or an inferior good? What feature of the function tells you?

6. Explain in words what the intercept (which is 60000) includes (or does not include).

7. Assuming the average annual family income (I_H) of CTI customers increases by $10000, how will the demand for CTI ovens change (give the numerical value of it, too)?

8. Assuming your advertising expenditures (A) are increased by $600000, how will the demand for CTI ovens change (give the numerical value of it, too)?

9. Assuming your competition announces a price (P_C) decrease of $100 for each of its microwave ovens, how will the demand for CTI ovens change (give the numerical value of it, too)?

10. A change in the quantity demanded of CTI ovens can only result from a change in which variable? Note: this is not asking what variable(s) will cause a “change in demand for CTI ovens”.

Answer 1

Part (i)

multivariate, linear, 1st degree, additive

equation contains more than two variable so it is multivariate. Function does not involve any log function or exponential so it is a linear function

Part (ii)

increase in average income increases demand for CTI ovens

Part (iii)

Part (iv)

increase in number of two-income household by 1 million increases the demand for CTI ovens by 5 millions units

Part (v)

the partial derivative of the function with respect to average annual income

increase in average income increases demand for ovens. This implies CTI ovens are normal goods

Part (vi)

intercept includes all the factors affecting demand (sales) for CTI ovens which are not quantifiable

Part (vii)

increase in average annual family income by $10,000 increases sales of CTI ovens by 1000 units

Part (viii)

increase in advertising expenditure by $ 600,000 increase sales of CTI ovens by 60 units

Part (ix)

fall in price of competing brand oven by $100 reduces demand for CTI ovens by 2000 units

Part (x)

A change in the quantity demanded of CTI ovens (depicted by movement along the demand curve) can only result from change in price of CTI ovens