Demand Estimation

Regression concepts:

1. Regression as fitting a straight line through a scattergram.2. Why the need for a formal method3. Why the minimize least squares rule instead of something else4. The infinite number of monkies regression5. How it is actually done--calculus

Regression tools: t values

1. Recall how to use the normal distribution to test hypotheses.2. Choosing the 5% tail, why.3. Recall the Z value for the 5% tail.4. For large numbers of observations, the t distribution is approximately normal.5. The rule of t > 2; and when it is that t>1.65 is an acceptable rule.

Regression tools: F distribution and Rsquared

1. Compare: t tests whether a single coefficient is significant, while F test whether the equation as a whole is significant.2. For both t and F most programs now print out the probability value, too.3. Rsquared is similar to F in that it measures the goodness of fit of the entire regression.4. Rsquared measured the percent of the variation in the dependent variable that is explained by the regression.

The regression equation; this is created in general terms by you from your theory, then you test it and acquire estimates of the parameters.

For example:

Y= a + bP + cX + dM + eL + u

Y= a + bP + cX + dM + eL + u

Reading regression output.

The "parameters" are the small lettered termsAlso called the constant and the coefficients.

For example, the term cX means that if the independent variable X were to increase by a unit, then the dependent variable would increase by c units.

Regression concept:

Your hypotheses (whether they are just hunches, guesses, or implications carefully derived from theory) are tested by the estimates of the parameters and the Rsquared.

For example: Hypothesis 1--Demand slopes downward. This theory implies that the parameter b is negative and significant.

Your Demand Estimation Project

"1. Apply Excel's Regression routine to estimate the demand fundtion for your produce," "where Observed demand = Constant + a*OwnPrice + b*Income,Percap + c*PriceofZ + d*Quality" ofProduct + e*Advertising + u (a random error term) Then apply the LN function to recalculate all your 6 variables into logs and redo. Which version had the better fit? "Of the two versions of regression you have done, use the nonlogged to answer these questions." 2. Is the equation significant overall? Which variables contribute significantly? Are each of these of the theoretically correct sign? 3. Is the Product Z a substitute product or a complement for your product? 4. Is your product an economically inferior product in this market or normal? "5. If Ownprice=24, Income=45, PriceofZ=12, Quality=50, and Advertising=37; what is then" the price elasticity of your product? Would you be wise to raise your price? Is your product considered a luxury good by this market?

Regression Anova Regular Data Multiple R 0.9656 R Squared 0.9320 Adj R Sqd 0.9211 Std Error 626.30 Observations 36 F Value 82.8 Significance 0.000

Regression Output, Regular Data Variable Coeff. StdError tValue PValue Intercept 305.8 531.6 0.57 0.560 Own Price -31.8 3.26 -9.74 0.000 Income 27.31 4.54 6.00 0.000 PriceZ 6.11 7.94 0.76 0.440 Quality 39.12 2.46 15.8 0.000 Advertsng 9.72 1.61 6.03 0.000

3. The product Z is a ________because the coefficient for PriceZ is positive.4. Your product is a(an)___________, because?

5. First calculate the quantity, Q: Then find dQ/dP =

It will follow the the price elasticity = ?Luxury good? Discuss.

Regression output, Log/Log Version Statistic Value pValue Multiple R 0.817 R Square 0.668 Adj RSqr 0.612 F value 12.083 0.000 Variable Coefficient Std Error t Value P Value Intercept 5.08 0.92 5.48 0.000 OwnPrice -0.30 0.07 -4.02 0.000 Income/cap 0.16 0.13 1.23 0.228 Priceof Z 0.02 0.066 0.44 0.660 Quality 0.55 0.09 6.14 0.000 Advertisng 0.27 0.09 2.77 0.009

You can check part of your work against this.

1. If the cost function for quality is C(Qu) = 11 +10.0*Qu and if the cost function for advertising is C(Adv) = 30 + 5.0*Adv; then which would make a better investment of an extra $100 by the company

2. Would it ever pay to substitute quality with advertising?

Part 2: Some examples of applications of demand estimates.

1. Filling in the unknown market areaDrawing: pizza shops around the city

but several areas uncovered.

2. Advising pricing policy. Contrast Millie's dress shop

with Acme Cement, Inc.

3. Investigate sensitivities:

a. J.D.Power example b. Is your product "upscale"? c. Ethnic tastes

4. Provide guidance to advertising. 5. Court cases and cross-elasticity.

6. "Bads" and tax policy.a. cigarette and alcohol studiesb. illicit drugs and price elasticity

7. Projections of firm demand.

8. Estimating demand for "free goods".

9. Test one's product's relation to the business cycle.

How things can go wrong with regression analysis:

1. Multicolinearity (highly correlated indepents).

2. Serial correlation (affects time series).

3. Heteroscedasticity ("Christmas tree residuals")

4. Omitted variables (sometimes a problem).

How to estimate a curvilinear curve:

A popular method is to start with a Cobb- Douglas demand function: Q = APbYc as an example.

Then convert this to logs

lnQ = lnA + blnP + clnY

The b an c are the price and income elasticities.

Review questions for the midterm: 1. Find the first derivative of Y = 120 - 2.3X + 33X2 - 21.4X3 + 3.1X5

2. Find the second derivative of the above function of X.

3. Find the first derivatives of each of the following:a. X(3X -1/X) b. b. 34X/(X2 - 110) c. G(H) where G=g(H3 - 2H) and H =h(X-2X2) 4. Find the values of X and Y the form an optimum of the function Z = 120 + 4.5X -3.4Y - 5.1X2 + 3Y2 - 3XY

6. Set up the LaGrangean function for each of the following:

a. ACME Inc. wishes to squeeze more production efficiency into its plant, but the board of directors insists that expenses not exceed 1200, when w=15 and r=20.b. NASA wants to minimize wing stress but maintain lift of at least 2000 pounds.

7. Find the point elasticity of the following demand functions:a. Q = 2000 - 45.5P when the P=33.

b. Q = 1000 - 45.5P + 30Y - 23Pz when the P= 33, Y=100; and Pz = 14

c. Q = 1000P-1.2Y3.0PZ1.2

8. In which of the above cases would the firm be advised to raise its price?

9. If price elasticity is greater than one in absolute value, and then if you lower your price--do you therefore increase your profits? 10. Define R Squared in your own words. 11. Which axiom is broken when indifference curves slope upwards? 12. Which axiom is broken when indifference curves cross?

12. If a regression coefficient for income, Y, has an insignificant t value but is nevertheless positive, is the product in question a normal good?

13. If the following variables are all entered as independent variables in a regression, which are likely to be highly colinear?

education, health status, income, smoking behavior, drinking behavior, air pollution.

14. Define serial autocorrelation in your own words.

15. Can there be such a thing as spatial autocorrelation? 16. Under indifference curve analysis, with well- behaved indifference curves, is it possible for a consumer to double his income but nevertheless consumer no more than before of all the goods?

17. What are the slopes (the expressions for them) of each of the following curves?:a. The budget line: b. b. An indifference curve:

18. Define a cross-price elasticity of demand and explain how its relation to the quantity demanded depends on its sign.

19. Does your hypothesis count as valid if its t value is significant but the F value is not?

20. Suppose you have estimated the following demand function for your company and it is easily and highly significant.

Q = 1000 - 42P + 33Y + 10Z

Then suppose that Y =7; and Z=12.Find the revenue maximizing price and quantity.