Hint: Look at demonstration problem 3-3 for help in solving this problem.

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1 Homework 3 Quantitative Demand Analysis Due: Tuesday 9/24 1) Textbook pg. 79 #3 (Baye pg. 115) Hint: Look at demonstration problem 3-3 for help in solving this problem. a. The own price elasticity of demand is simply the coefficient of ln P x, which is 1.5. Since this number is more than one in absolute value, demand is elastic. b. The cross-price elasticity of demand is simply the coefficient of ln P y, which is 2. Since this number is positive, goods X and Y are substitutes. c. The income elasticity of demand is simply the coefficient of ln M, which is Since this number is negative, good X is an inferior good. d. The advertising elasticity of demand is simply the coefficient of ln A, which is 1. 2) Textbook pg. 81 #9 (Baye pg. 117) Hint: You may use the rule of thumb when evaluating if a variable is statistically significant a. The t statistics are as follows: ; ; and. b. Since the coefficient estimate,, is not statistically different from zero. Since, the coefficient estimate,, is statistically different from zero. Finally, since the coefficient estimate,, is not statistically different from zero. c. The R-square tells us that 35 percent of the variability in the dependent variable is explained by price and income. 3) Data for 3 states for the Kalamazoo Brewing Company (KBC) is available on the course website under the file title HWData.xlsx. Answer the following questions using this data. a. Print the regression output for each of the states. Use quantity as your dependent variable, and price and income as your independent variables.

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3 b. Provide an economic interpretation for each of the regression results. Example for answer for Mississippi: The marginal effect of a change in price, i.e. if there is a one unit increase in price, causes quantity demanded to decrease by.792 units, ceteris paribus. This shows that price and quantity demanded are negatively related. The marginal effect of a change in income, i.e. if there is a one unit increase in income, causes quantity demanded to increase by 7.45 units, ceteris paribus. This shows that income and quantity demanded are positively related (normal goods). c. What do you expect to happen to the demand for KBC brews as average incomes rise across the United States? Because the coefficient for income is positive and statistically significant for all three regressions we can say with confidence that KBC brews are normal goods. Further, as incomes rise we can expect the quantity demanded of KBC to increase in each state. d. Perform a natural log transformation on the variables for Wisconsin and re-estimate the demand equation to answer the following: To take the natural logarithm of the variables use the function =ln(xx) where XX denotes the cell of the variable you are transforming. After that, use the transformed data to run the regression. The first few observations are included below next to the regression output to double check that you transformed the data correctly.

4 i. What is the price elasticity of demand? What can we say about demand for beer in Wisconsin (elastic vs. inelastic)? As in #1, the coefficients are elasticities when we have a ln transformed equation. Thus, the own-price elasticity for KBC is Because this number is less than 1 (in absolute value), and statistically significant, we can say that demand is inelastic. Further, we can interpret this result in the following way: A one percent increase in price will cause quantity demanded to decrease by.174 percent, ceteris paribus. ii. What advice would you give to KBC if they wished to raise revenues? Homework 2 asked you to summarize the relationship between own-price elasticity and total revenue, and this is an application of that. Because demand is inelastic for KBC brews they should consider raising their price if they wish to increase their revenues. iii. What is the income elasticity of demand? The income elasticity of demand is simply the coefficient on income since this is a ln transformed equation. Thus, the income elasticity of demand is.838. Because this number is positive and statistically significant we can say that KBC brews are a normal good. Further, we can interpret the results in the following way: A one percent increase

5 in income will cause quantity demanded to increase by.838 percent, ceteris paribus.