Qh = 60,000 - 40 Ph + 20Pc + 5H + .10Ih + .0001Ah Qh: Annual Sales Ph: Price of
ID: 2439843 • Letter: Q
Question
Qh = 60,000 - 40 Ph + 20Pc + 5H + .10Ih + .0001AhQh: Annual Sales Ph: Price of deluxe model Pc: price of competing-brand oven H: Number of two-income households (in millions) in this income bracket Ih: Average annual income of household in this bracket 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. 1. Characterize this function by circling all in the following univariate, bivariate, multivariate, linear, exponential, degree, additive, multiplicative, linearly homogeneous 2. What is the numerical value of the partial derivative of sure to also include the +or-sign. Note: I do not want logarithmic, curvilinear, 1 degree, 2nd degree, 3d the function with respect to average annual income (be the symbol for this partial derivative)? 3. Write the mathematical symbol representing the coefficient of the number of two-income households. (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 (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 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 are increased by $600000, how will the demand for CTI ovens change (give the numerical value of it, too)?
Explanation / Answer
1) Multivariate; linear
Given function contains more than two variable so it is multivariate. Function does not involve any log function or exponential so it is a linear function.
2) Qh = 60,000 - 40 Ph + 20Pc + 5H + .10Ih + .0001Ah
dQh/dIh = + .10
So, numerical value is 0.10
3) Qh = 60,000 - 40 Ph + 20Pc + 5H + .10Ih + .0001Ah
dQh/dH = 5
4) Qh = 60,000 - 40 Ph + 20Pc + 5H + .10Ih + .0001Ah
Qh' = 60,000 - 40 Ph + 20Pc + 5(H + 1) + .10Ih + .0001Ah
Qh' = 60,000 - 40 Ph + 20Pc + 5H + 5 + .10Ih + .0001Ah
Qh' = Qh + 5
So, demand for CTI increases by 5.
5. Qh = 60,000 - 40 Ph + 20Pc + 5H + .10Ih + .0001Ah
Increase in income i.e. Ih, causes increase in demand of Qh. This implies CTI ovens are normal good.
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