02 Jun Question Each question is worth 10 pts. Show your working. Unless otherwise stated each part of each question is worth 5 pts.
Question
Each question is worth 10 pts. Show your working. Unless otherwise stated each part of each question is worth 5 pts.
1.(Supply and Demand)
(a) Suppose the estimated market demand for oil is Q = 100 – 3P + Pg and the supply curve is Q = 15 + 2P, where Q is millions of barrels of oil, P is the price of oil in $ per barrel, and Pg is the price of natural gas in $/litre. Find the equilibrium P and Q when the price of natural gas is Pg = $10. Find the new equilibrium when the price of natural gas decreases to Pg = $5. Illustrate your results in a diagram. Label the axes and the demand and supply functions and show the equilibrium prices and quantities.
(b) Coincidentally, just as the price of natural gas falls, there is increased turmoil in oil-producing countries in the Middle East, causing an inward shift in the supply curve for oil. What is the combined effect of the change in Pg and the shock to oil supply on the equilibrium price and quantity of oil? (i.e., what can we say about the direction of change of equilibrium quantity and price?) Use a diagram in your explanation.
2.(Elasticity)Read the New Yorker article, “Amazon’s Failed Pitch to Authors,” available at the following link: www.newyorker.com/business/currency/amazons-failed-pitch-authors
(a)Assuming that Amazon’s internal figures are correct, compute the arc elasticity of demand for the change in price from $14.99 to $9.99 by using the corresponding quantity numbers from the article.
(b)The literary agent, Brian DeFiore, worries that Amazon might continue to lower prices, to perhaps as low as $4.99. Assume that the demand curve for e-books is linear and that Amazon maximizes revenue on its e-book sales. What price would Amazon charge? [Hint: If you assume demand is linear you can work out its formula from the data in the article.] How would your answer change if the demand curve were of the constant-elasticity form (as in Q&A 3.2)?
3. (Regression I): Figure 3.6 in the textbook illustrates two advertising regressions and Table 3.2 shows the regression results. Sales is the dependent variable and Advertising is the explanatory variable. The underlying data is as follows:
Adv.
.5
1
2
3
4
6
8
10
12
14
16
Sales
4.0
5.1
6.2
7.4
8.8
9.5
11.0
11.4
11.8
12.2
12.7
a)Use the scatter plot Trendline option in Excel to run a linear regressionand a quadratic regression (i.e. a polynomial function of order 2). Sales is the dependent variable. Therefore, using Trendline, put advertising in column A and sales in column B. Cut and paste (electronically, not manually) the Excel spreadsheet below, with both diagrams in the same spreadsheet. Verify that you get the same coefficients as shown in Table 3.2 (after rounding). Report the R2 statistics.
b)Based on Figure 3.6, Table 3.2, and the regression reported in part a, provide three reasons why the quadratic specification should be preferred. (The reasons should be based on the figure or the statistical regression results.)
4. (Regression II) At the end of Chapter 3, question 7.2 on p. 83 provides some data regarding ice cream sales.
a)Using the data in question 7.2 estimate the demand function for Tropical Cream ice cream as a function of its own price and the price of green mango ice cream. You may use the LINEST function described on pp. 64-65 to do this. Alternatively, if you use the Windows version of Excel, you may use the regression tool described in Appendix 3 (p.84). If you have a Mac you may wish to download a regression module for Mac Excel as described in footnote 24 on p. 84. Cut and past the regression output into the space below. (No diagram is needed.)
b)Based on the regression in part a, state the equation of the estimated regression line, the standard errors, the t-statistics, and the R-squared statistic. (If you use the Windows Excel regression tool this output should be clearly shown in part a.) Just restate that information here in a paragraph. Is green mango ice cream a substitute or complement for tropical cream ice cream? Explain briefly.
c)
5. (Consumer Choice). Laura has a utility function given by U(X, Y) = 4X0.5Y0.5. The current prices of X and Y are $25 and $50, respectively. Laura currently has an income of $750 to spend on X and Y.
a)If Laura is currently consuming 10 units of X, is she maximizing her utility? Use the last dollar rule given by equation 4.7 on p. 105.
b) Illustrate the situation described in part a) in a diagram similar to Figure 4.8 in the text. Is there anything Laura can do to increase her utility? Explain briefly.
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