Final_spring06 - Economics 313-1 Talia Bar Final...

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1 Economics 313-1 Cornell University Talia Bar Spring 2006 Final Examination This exam consists of three sections. Answer each section in a separate blue book and label each blue book clearly. The exam is worth 145 points. You will have 150 minutes (2.5 hours) to complete it. Allocate your time wisely between the sections. The exam is closed-book, but you may use a calculator. Good luck. Section I (50 points) Question 1 (30 points) (Consumer theory) Every school in some state has $5000 to spend on computers (C) and other goods (Y). Prices of these two commodities are P C =20, P Y = $1. Each school has preferences for computers and other goods that can be represented by U(C,Y) = AlnC+Y . where A>0 is some constant value. The State Education Commission has decided that it is desired for each school to consumer at least C=100 units of computers. The schools interests are not necessarily aligned with those of the State Education Commission. The Commission has no funds to spend on this program and the money for any policy would need to come from taxing the schools. The Commission is considering the following ways to induce schools to consume exactly C=100 units of computers. Plan 1: The state will provide C=100 units of computers to each school and tax them a lump sum of $T (i.e. deduct T from each high school’s budget) to cover the cost of the C=100 units of computers provided to that school. Assume the school cannot sell the units of computer provided by the state. Plan 2: The state will give each school $S as a lump sum subsidy (i.e. increase each high school’s budget by S) and will levy a tax of $t per dollar spent on other goods (i.e. the price of Y becomes $(1+t)). The state will choose S and t such that the tax revenues from each school exactly cover the subsidy given to that school, and such that with its new budget the school will choose to consume C=100 units of computers. (a) Write the utility maximization problem of a school if the state does not intervene in the school’s budget spending. (b) How many units of computers will the school purchase without any intervention? (Your answer should depend on the parameter A).
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2 (c) For what values of the parameter A will no intervention result in consumption of at least 100 units of computers? If A=1000 how many units of computers will be demanded? From now on (for parts d-i) assume A=1000. (d) If plan 1 were adopted, what tax T is needed to finance the C=100 units of computer given to a school? How many units of other goods will the school purchase? (e) Show on the same graph the schools budgets, indifference curves and optimal choices with no intervention and with plan 1.
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Final_spring06 - Economics 313-1 Talia Bar Final...

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