Explain the attached questions
install . packages("wooldridge") 2 library(wooldridge) 3 help (package = "wooldridge") 4 data( 'catholic') Problem 4: (version of Wooldridge Chap. 7 C.12) Use again the data in CATHOLIC. The model of interest is math 12; = Bo + B,cathhs; + ui where cathhs is a binary indicator (dummy variable) for whether a student attends a Catholic high school or not. 1. Do an exploratory analysis of the variables in the model above as well as the variables Ifaminc, motheduc, and fatheduc. 2. Estimate the above equation by OLS in R and interpret the coeffi cients. 3. Which assumption(s) of CNLR troubles you most in this model? 4. Now add the variables hsgrad, Ifamine, motheduc, and fatheduc to the regression from part (2) and interpret the estimates. How many observations are used in the regression? What happens to the coeffi cient on cathhs? 5. Return to the simple regression of math12 on cathhs, but restrict the regression to observations used in the multiple regression from part (5). Do any important conclusions change? 6. Explain how you could allow for the effect of cathhs vary with each of the other independent variables in (5) . Reestimate the model accordingly.Question 1: eBay's Recommendation It is hard to imagine that anyone is not familiar with eBay, the most popular auction website by far. In a typical eBay auction a good is placed for sale, and each bidder places a 'prosy bid' which eBay keeps in memory. If you enter a proxy bid that is lower than the current highest bid, than your hid is ignored. If, however, it is higher, then the current bid increases up to one increment (say, 1 cent] above the second highest proxy hid. For example, imagine that three people have placed bids on a used laptop of $55, $93, and $112.. The current price would he $9331, and if the auction ended the player who bid $112 would win at a price of $93.01. If you were to place a bid of $13.45 then the player who bid $112 would still win, but at a price of HIE-=16, while if your bid was $123, then you would win at a price of $112.01. Now consider eBay's historical recommendation that you think hard about the value you impute to the good, and that you enter your true value as your bidno more, no less. Assume that the value of the good for each potential bidder is independent of how much the other bidders value it. (a) Argue that bidding more than your valuation is weakly dominated by actually bidding your valuation. (b) Argue that bidding less than your valuation is weakly dominated by actually bidding your valuation. (c) Use your analysis to make sense of eBay's recommendation. 1Would you follow it? Consider a situation where a single upstream rm acts as a monopolist and supplies two downstream rms that compete in quantities. The downstream market faces an inverse market demand curve of p=100q1\"q where 1.319 and q? are downstream rm 1 and 2's quantities, respectively Both rms in the downstream market must purchase one unit of the upstream markets good as an input and pay an additional constant marginal cost of CD = 20 for each unit of the good they produce. The upstream rm also faces a constant marginal cost of c\" = 20. :1) Find the equilibrium prices and quantities in both the upstream and downstream markets. b) Suppose the upstream rm could merge with downstream rm 1 for a xed fee of 250. In doing this, it would also foreclose on downstream rm 2. Would this merger be protable? Why or why not? (3) Rather than merging with either rm, suppose the upstream rm could franchise out to each of the downstream rms. Find the equilibrium prices and quantities for both the upstream and downstream markets as well as the franchise fee. QUESTION 1 There are three households in a community. Their individual marginal benet for hours (H) per week of public television is given by MBI=30-H, M32: 602H and MB3=70H. Suppose that public television is a pure public good that can be produced at a constant marginal cost of $100 per hour. (a) Sketch the three marginal benet schedules and the aggregate marginal benet schedule. Draw the marginal cost schedule, and find the efficient level of provision for hours per week of public television. What would be the net benefit to the community if the efcient number were provided? (b) Suppose that the local government nances the hours per week of public television out of taxes. Show that the local government can achieve the social optimum by setting the correct tax prices 1'1, 12 and t3 on individuals 1, 2 and 3, respectively. What taxes should it set? (c) Explain why a set of tax prices such as the one proposed in (b) is unlikely to provide the proper incentives for individuals to reveal their true preferences for the public good
