Analyze the demand function for Paradise Lake's properties in problem C5, page 83.Please also read "What is a Symbol" located in the folder with this assignment.

This function is:

Q_L= 3536 - .5P_L+ .2P_C+ .008I + .0001A

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 income (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 advertising (the numerical value of this coefficient is +.0001, but the answer you give is to be the representing this partial derivative).

4.Assuming there is a $200 increase in the price of Paradise Lake lots (P_L), what change in quantity demanded of Paradise Lake lots will result (give the numerical value of it, too).

5. Are Paradise Lake lots a normal or an inferior good?What feature of the function tells you?

6.Explain in words what the intercept (which is 3536) includes (or does not include).

7.Is there a direct or is there an inverse relationship between demand for lots (Q_L) and advertising expenditures (A)?What feature of the function tells you?

8.How will demand for Paradise Lake's lots (Q_L) change in response to a $1000 decrease in the price of competing lots (P_c) (give the numerical value of it, too)?

9.How will demand for Paradise Lake's lots change in response to a $1000 decrease in income (I) (give the numerical value of it, too)?

10.What variable do I need to change in order to achieve a change in the quantity demanded (Q_L) of Paradise Lake lots?

WHAT IS A SYMBOL (as it relates to Assignment 7)? A symbol is a shorthand way of representing something else (OK -- this is not Webster's definition). I can write, "find the price of an item and square it" or I can simply write P x2 (assuming you let me get away with saying that X is the item). Suppose I have a function with one variable, say Z, whose dependent variable is Y. If I want the first derivative of this function, I can ask you to find the first derivative, I can also ask you to find dy/dz or perhaps I get really lazy, I can ask you to find Y'. Want the derivative of a derivative, that is, a second derivative? Find d 2y/dz2 or being lazy, I could simply say, find Y'' (I claim NO originality for these symbols --- they are very standard ways of indicating derivatives of a function with only one independent variable). NOW in Power Point Lesson 15, we encounter the very common Multivariate, additive, linear, 1st degree demand function (multivariate because the function has several independent variables that are added together. The variables are all raised to the power of one, thus linear and 1st degree). In this lesson you also get introduced to the concept of a partial derivative. Why partial? The concept of a total derivative means that you want the incremental (marginal) influence on demand of a simultaneous incremental change in all of the independent variables. This is a mess, and does not allow you to do analysis of the influence of a change in only ONE variable. It is useful to find the incremental (marginal) influence on demand of a change in only one variable of interest to you. Suppose Q = [ a function of several variables, one of which is H]. If you are interested in the marginal influence of a change in H on dependent variable Q, how do you state what you want by using a symbol? You cannot use dQ/dH because then H would have to be the only independent variable in the equation. Mathematicians have a very special symbol for a partial derivative. They would ask you to find Q/H. This symbol sort of looks like a backward 6. See footnote 23 on page 59 of the Truett text for an example of its use in a point elasticity. This symbol means find the marginal influence on the demand for Q of an incremental change in H, assuming there is no change in any of the other independent variables at the same instance . What if advertising expenditures were one of the variables in the multivariate function. Then you would find Q/A. This symbol means find the marginal influence on the demand for Q of an incremental change in A, assuming there is no change in any of the other independent variables. The amount of the change in demand caused by the change in the variable of interest and the direction of the change is very easy to calculate. Suppose the variable whose influence you are assessing is A (advertising). Assume this variable is in the equation as + .25A. Here the partial derivative is Q/A = + .25. This says for each $1 increase in advertising expenditure, demand for the product increases by .25 units. Marketing types would jump for joy if their advertising had this much influence! Think of it! Spend $1000 on advertising and you have an increase in sales of 250 units. However, the knife cuts both ways: have a $1000 decrease in advertising expenditures and you will have a 250 unit decrease in sales. By the way, if a multiple linear regression equation is estimated of this type of multivariate function, the estimated coefficients of the variables ARE estimates of the partial derivatives of the respective variables