Sample_Midterm_Solutions[1]

Sample_Midterm_Solutions[1] - PART I QUESTION 1 New York...

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PART I – QUESTION 1 New York State allocates its $1 million transportation budget between maintenance of rail lines and maintenance of highways (both are measured in miles).The cost of maintaining one mile of rail is $50 and the cost of maintaining one mile of highway is $100. a) (3 points) Putting rail lines on the x-axis and highway miles on the y-axis illustrate New York State’s budget set. What is the opportunity cost of maintaining an additional rail mile? Show (algebraically) that NY State can afford to maintain 6000 miles of highway and 8000 miles of rail line. Opportunity cost = Px/Py = 50/100 = 0.5 highway miles per rail mile Cost of (8000, 6000) = (50)*8000 + (100)*6000 = 400000 + 600000 = 1000000 So (8000,6000) is affordable b) (4 points) Suppose that NY State’s MRS at (8000,6000) is 1. Is (8000,6000) NY State’s best bundle? Why or why not? Briefly explain your answer. If not will NY State choose to spend more or less money on rail maintenance? Illustrate the indifference curve through (8000,6000) in your diagram from part (a). (8000,6000) is not the optimal bundle, because the MRS is greater than the price ratio(slope) at that point. Since MRS>(Px/Py) NY State will choose to spend more money on rail mentainance. Rail miles Highway Miles 20000 10000 MRS = 1 Slope= 0.5
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Suppose that the federal government would like to encourage the states to spend more money to maintain rail lines. The federal government is willing to provide a subsidy of $10 per mile of rail line maintained above 10,000 miles. Hence NY State must pay $50 per mile for each mile up to 10,000 and $40 per mile for every mile thereafter. c) (4 points) In a new diagram illustrate NY State’s budget set given the Federal government’s offer of a subsidy. Be sure to include your budget line from part (a). d) (4 points) If before the subsidy program was announced NY State had planned to maintain 9,000 miles of rail then will it choose to participate in the subsidy program? Use your diagram to explain your answer. The new budget set does not contain points that are strictly better then the old optimal point (i.e. that have more of both goods than the old optimal point had). The answer thus depends on the particular form of the utility function. As you can see in the diagram, there exists a scenario in which NY State will be better off by participating and there exists one in which they will not be better off by participating. Rail miles Highway Miles 20000 10000 10000 22500 9000
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PART I – QUESTION 2
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c) 168 120 12 24 10 12 120 = = = = b l d) At the substitution point, MRS should be equal to 12 10 12 120 12 = = = l l MRS We now need to find the b-coordinate of a point on the initial indifference curve that has l=10. ( ) 142
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Sample_Midterm_Solutions[1] - PART I QUESTION 1 New York...

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