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Demand Estimation

Demand Estimation. Regression concepts: 1. Regression as fitting a straight line through a scattergram. 2. Why the need for a formal method 3. Why the minimize least squares rule instead of something else 4. The infinite number of monkies regression

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Demand Estimation

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  1. Demand Estimation

  2. Regression concepts: 1. Regression as fitting a straight line through a scattergram. 2. Why the need for a formal method 3. Why the minimize least squares rule instead of something else 4. The infinite number of monkies regression 5. How it is actually done--calculus

  3. 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.

  4. 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.

  5. 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

  6. Y= a + bP + cX + dM + eL + u Reading regression output. The "parameters" are the small lettered terms Also 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.

  7. 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.

  8. Your Demand Estimation Project

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

  10. 5. First calculate the quantity, Q: Then find dQ/dP = It will follow the the price elasticity = ? Luxury good? Discuss.

  11. You can check part of your work against this.

  12. 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?

  13. Part 2: Some examples of applications of demand estimates. 1. Filling in the unknown market area Drawing: pizza shops around the city but several areas uncovered. 2. Advising pricing policy. Contrast Millie's dress shop with Acme Cement, Inc.

  14. 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.

  15. 6. "Bads" and tax policy. a. cigarette and alcohol studies b. 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.

  16. 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).

  17. 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.

  18. 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.

  19. 3. Find the first derivatives of each of the • following: • X(3X -1/X) • b. 34X/(X2 - 110) • 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

  20. 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.

  21. 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?

  22. 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?

  23. 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.

  24. 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?

  25. 17. What are the slopes (the expressions for • them) of each of the following curves?: • The budget line: • 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?

  26. 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.

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