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# could you please figure out question (a) of problem no.2 ?

could you please figure out question (a) of problem no.2 ?

EEP 145 Problem Set 2 Due Oct 8 1. As part of the California High Speed Rail System, the Caltrain tracks from SJ to SF will be upgraded to support modestly higher speeds. A key question is what speed should they be upgraded to. The current speed (80 mph) is unacceptably slow, but the top speed of the trains (220 mph) may not be appropriate for a dense urban/suburban area. Suppose that train ridership is P = 100 S , where P is total ridership (passengers) and S is the speed that the train will run at (mph). Suppose that operating at speed S costs C = 50 S + 3 S 2 (note that this cost is independent of the number of passengers that ride). Further suppose that each passenger that rides is willing to pay up to \$3.50 + \$0.02 S to ride the train and that each passenger that rides the train saves other highway commuters \$7 in congestion costs. Finally, suppose that higher speeds create more noise for houses located next to the tracks, and that the total cost of this noise is N = \$3 S 2 . a. Suppose that Caltrain intends to set the fare at \$3.50 and that, given this fare, their goal is to choose speed S to maximize revenue (3.5 P ) minus costs ( C ). What are marginal revenue (i.e., d (Total Revenue)/ dS ) and marginal cost (i.e., d (Total Cost)/ dS ) as functions of S ? What value of S will Caltrain choose? b. Now suppose that Caltrans instructs Caltrain to also take into account congestion relief benefits when calculating total benefits and choosing the optimal value of S . The fare is again fixed at \$3.50. What are the marginal benefits as a function of S ? What value of S will Caltrain choose? c. Finally suppose that the state instructs Caltrain to also take into account all costs and benefits when choosing the optimal value of S . What are the marginal benefits and marginal costs as functions of S ? What value of S will Caltrain choose? 2. Suppose that soybean yield (measured in bushels per acre) is determined by the model: ࠵±²³´ = ! + ! ࠵±²³´µ´¶±² + where ࠵±²³´ ࠵±²³´µ´¶±² ] = ! + ! ࠵±²³´µ´¶±² In this model Y = , X = , and u represents other factors that affect yield . The agricultural researcher is interested in the relationship between
fertilizer and yield. a. Consider a simple regression of yield on fertilizer . Suppose that regression generates a positive estimate of the slope coefficient β 1 . Is it valid to conclude that farms that use more fertilizer appear to have higher yields? b. Now consider the term u . What kinds of factors could be contained in u ? c. Will a simple regression of yield on fertilizer uncover the ceteris paribus effect of fertilizer on yield? Explain. 3. Suppose you are interested in estimating the effect of hours spent in an SAT preparation course ( hours ) on total SAT score ( sat ). The population is all college-bound high school seniors for a particular year. In this model Y = sat and X = hours . a. Suppose you are given a grant to run a controlled experiment. Explain how you would structure the experiment in order to estimate the causal effect of hours on sat . b. Consider the more realistic case where students choose how much time to spend in a preparation course. Suppose you have student- level data on sat and hours (i.e., each observation in your data is one student). You intend to run a multiple regression to estimate the causal effect of hours on sat . Name at least one control variable that you would like to include in the regression (in addition to hours ). Why are you including it?

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