Chapter 3 homework Numbers 6, 7, 12 Review session: Monday 6:30-7:30 Thomas 324

Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis

P Q Q D D LinearLog Linear Graphical Representation of Linear and Log-Linear Demand P

Let’s try some homework (number 2) The demand curve for a product is given by Where P z = $400 What is the own price elasticity of demand when P x =$154? Is demand elastic or inelastic? What happens to TR if it decided to charge a price below $154? What is the own price elasticity of demand when P x =$354? Is demand elastic or inelastic? What happens to TR if it decided to charge a price below $354? What is the cross price elasticity of demand when P x =$154? Are the goods compliments or substitutues?

X Y What does the demand curve look like? Regression Line

Regression Analysis One use is for estimating demand functions. Important terminology and concepts: n Least Squares Regression: Y = a + bX + e. e are the “dotted” lines from the dot to the regression line Called the error term (mean of zero) Best Fit Regression Line minimizes the sum of squared errors Best Fit 

More terminology n Standard error Measures how much each coefficient would varies from the mean of the population n Confidence Intervals Give you the upper and lower bounds for the “true” coefficient. Calculated coefficient lies in the middle of this interval 95% confidence intervals says that we are 95% sure that the “true” value will lie between these values

Rule of Thumb Confidence Interval Calculation The  is the standard error to the coefficient

Still more terminology n t-statistic Ratio of parameter estimate to the standard error Large???  true value of the variable is NOT zero Rule of thumb  if greater than or equal to the absolute value of 2 then the parameter estimate is statistically different from zero n How good does the line fit??? R-square or Coefficient of Determination –Fraction of the total variation in the dependent variable explained by the independent variables –Ratio of the Sum of Squared Errors to the total sum of squared errors –Range is from 0 to 1

And more terminology Adjusted R-square n Adjusts for the number of observations as well as number of coefficients F-statistic n Provides a measure of the total variation explained by the regression relative to the total unexplained variation n Look at the number and the significance of the value F-statistic = Significance F = Says there is less than 0.12% chance that the data was fit by accident If F-statistic significant at 5% or less then we can say that the regression is statistically significant

An Example Using a spreadsheet we can estimate the following log-linear demand function.

Summary Output

Let’s try some homework (number 15) As the newly appointed “Energy Czar”, your goal is to reduce the total demand for residential heating fuel in your state. You must choose one of three legislative proposals designed to accomplish this goal: (a) a tax that would effectively increase the price of residential heating fuel by $2; (b) a subsidy that would effectively reduce the price of natural gas by $1; (c) a tax that would effectively increase the price of electricity (produced by hydroelectric facilities) by $5. To assist you in your decision, and economist in your office has estimated the demand for residential heating fuel using a linear demand specification. Based on this information, which proposal would you favor? Explain.

Summary Output