ECON HW #3 Final

Ilana Berger, Jessica Gonsalves, Sankalp Khare, James Lee, Cesar Valiente Professor Kirsten Daniel Microeconomics for Management Group Homework # 3 Problem # 1 You are the marketing manager of a firm that produces Titanium and sells this metal to two distinct kinds of customers: aircraft producers and golf club manufacturers. Demand for Titanium by these two market segments is quite different, as described by the respective price equations: PA = 10 - QA./600 and PG = 12 - QG./100, where annual quantities are in thousands of pounds and prices are in dollars. Your firm estimates the marginal cost of titanium production at $4 per pound. a) What is the optimal price and quantity for the aircraft segment? P A = 10 - Q A ./600 MR (Marginal Revenue) = MC ( Marginal Cost) 10 - 2Q A /600 = 4 -2Q A /600 = -6 -2Q A = -3600 Q A = 1,800 => Q A = 1800 ( Optimal Quantity) Using Q A = 1800 in eq 1, we get P A = 10 - 1800/600 P A = $7 ( Optimal Price) b) What is the optimal price and quantity for the golf segment? P G = 12 - Q G /100 —---eq 1 MR G (Marginal Revenue) = MC ( Marginal Cost) 12 - 2Q G /100 = 4 => Q G = 400 ( Optimal Quantity) Using Q G = 400 in eq 1, we get

P G = 8 (Optimal Price) Problem # 2 Gold Trackers monitors the price of precious metals, and has daily data on prices and sales of gold for the past several years. One of their new MBA financial wizards has estimated the following relationship for gold sales in the past year of trading (250 observations): Q = 4000 – 0.01 P + 1.5 I – 1.25 X + 2.0 S (857) (0.002) (0.65) (0.44) (0.48) R 2 = 0.96 Where Q = daily sale of gold in ounces, P is the price of gold in dollars per ounce, I is the most recent one-month report on US CPI inflation (in percent), X is an index on the exchange rate of the US dollar compared to seven other currencies, and S is the market price of an ounce of silver in dollars. Standard errors are in parentheses. a) Evaluate the results of this regression. Compute t-statistics and F-statistic. T-Statistics: Degrees of Freedom = (N-k) = 250 - 5 = 245 … using the T table we find a t-statistic for 95% confidence interval of 1.96 P= 0.01/0.002 = -5 … -5 > 1.96 = passes 95% significance S= 2/0.48 = 4.16 … 4.16 > 1.96 = passes 95% significance I= 1.5/ 0.65 = 2.307 > 1.96 = passes 95% significance X= 1.25/ 0.44 = 2.841 > 1.96 = passes 95% significance F-Stat: ((R 2 ) / (K-1)) / ((1-R 2 ) / (N-K)) = 0.96/ (5-1) / (1-0.96) (250 -5) = (0.96/ 4) / (0.04/245) = 0.24 / 0.00016327 = 1470 F-Stat = 1470 When k-1 =4 , Df: N - k =245 critical F in 95% fractile is 2.37 When k-1 =4 , Df: N - k =245 critical F in 99% fractile is 3.32 When we look at the information above, we can see the value of R 2 = 0.96 and this means that 96% of the variation in the explanatory variables is explained, which means that a

Problem # 3 In early 2002, Mrs. Smyth’s, a Chicago based food company, initiated an empirical estimation of demand for its gourmet frozen fruit pies. The firm wants to formulate pricing and promotional plans for the future on the basis of historical data, and management is interested in learning how pricing and promotional decisions might affect sales. Mrs. Smyth’s has been marketing frozen fruit pies for several years, and its market research department has collected quarterly data over two years for six important marketing areas, including unit sales quantity, the retail price charged for the pies, local advertising and promotional expenditures, and the price charged by a major competing brand of frozen pies. Statistical data published by the U.S. Census Bureau on population and disposable income in each of the six market areas were also available for analysis. It was therefore possible to include a wide range of hypothesized demand determinants in an empirical estimation of fruit pie demand. The underlying data are posted as a word document on Canvas. A linear regression of the following form was run: Q it = b 0 + b 1 P it + b 2 A it + b 3 PX it + b 4 Y it + b 5 Pop it +b 6 T it The subscript i indicates the regional market from which the observation was taken, whereas the subscript t represents the quarter during which the observation occurred. Where Q is the quantity of pies sold during the t-th quarter P is the retail price in dollars of Mrs. Smyth’s frozen pies A represents the dollars spent on advertising PX is the price, measured in dollars, charged for competing Y is dollars of disposable income per capita Pop is the population of the market area T is a trend factor (2000 – 1= 1, ..... , 2001 – 4 = 8) a) Interpret the signs and magnitudes of all the coefficients. Constant - Constants do not generally have a significant interpretation. However, in the case of the above coefficients, we can use it as the level of sales if we leave all the other variables equal to 0. Price - The price coefficient shows how the quantity demanded changes with variations in its own price. As we can expect, the sign is negative and this means that if the higher the price, the lower the quantity demanded will be. Specifically, we can see that if P goes up by $1, quantity demanded will decrease by an average of 127358 units. Advertising - This tells us the reaction of the quantity to changes in the advertising spending. Usually, the more money that is spent on advertising, the more we can sell. Specifically, with $1 of each additional advertising spend increases the sales by an average of 5.35 units.

Price of Competitors - This coefficient shows the effect of the price of competitors on our sales. Here the coefficient is positive so from this we can tell that the two goods are substitutes and are competing with one another for market share. Specifically, if the competitor increases price by $1, our sales will increase by an average of 29403 units. Disposable Income - This coefficient shows us how change in the disposable income per capita can affect the sales. For each additional $1 disposable income, our sales will go up by 0.324 units on average. Overall, this is not very statistically significant in this case. Population - This measures how the size of the population affects the sales. On average, the addition of one person will increase sales by 0.0239. Trend - This coefficient relates to time passing and how it affects demand overall as it evolves over time. We can see that demand increases by 4395.6 units per year on average. The trend coefficient is generally insignificant here. b) Interpret the coefficient of determination (R 2 ) for the Mrs. Smyth’s frozen fruit pie demand equation. R 2 , which is the coefficient of determination measures how much of the variability of the dependent variable is captured and explained by the equation. Here, R 2 is equal to 0.896. This means that 89.6% of the dependent variable, which is sales, is explained by the variables in the equation. c) Use the regression model to estimate 2002 – 1 unit sales in the Washington, DC-Baltimore, MD, market under the following assumptions: P = $7.20 A = $30,000 PX = $6.00 Y = $43,000 Pop = same as in prior period (see underlying data as posted on EEE). Q it = b 0 + b 1 P it + b 2 A it + b 3 PX it + b 4 Y it + b 5 POP it + b 6 T it Q it = 646,825.8 + (- 127,358.3 x 7.2) + (5.351 x 30,000) + (29,403.91 x 6) + (0.3243 x 43,000) + (0.0239 x 7,782,654) + (4,396.644 x 9) Q it = 306,797.0465 unit sales d) Calculate the demand elasticity under the above conditions at a price of $7.20. E p = (∂Q / ∂P) x (P / Q)

b= -2.5 => P= a - b(Q) 200 = a - (2.5) (400) 200 = a - 1000 a=1200 Demand Equation: P = 1200 + 2.5(Q) When operating at the extreme of the curve, they are far from the current price and quantity, such extreme numbers may not give us reliable predictions. Also at the very ends of the curve, it is no longer linear and we might need additional data to estimate the exact points. b) The survey firm also reports that if per capita income changes, Rail Tours can expect a large change in bookings. In particular, if per capita income falls by 1%, then bookings will tend to fall by about 2%. Are tour packages normally good? Explain. Tour packages are not normal goods. When per capita disposable income rises, demand also rises. Vice versa, when income goes down, so does demand because they are positively correlated. c) If you were responsible for making a forecast for bookings, would you accept this forecast as is? Or would you want additional information about demand? Explain. In order to make the forecast for bookings more accurate, we would want more information on other demand relevant factors. These would include substitutes that affect our demand along with the effects of seasonality. We would also want more data on the regression model statistics because it is difficult to tell whether these survey results are significant. By having this additional information we would be able to to change the capacities of the tour according to the anticipated demand.