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problem on Legislature budget

XY School District has a large number of students in need of remedial instruction. The superintendent of XY School System can allocated her budget between purchasing X units of remedial instruction at a price of $2,000/unit and spending an amount ($Y) on all other school activities.  (For the purposes of this problem, assume that “all other school activities” can be viewed as a composite commodity with a per-unit price of $1,000.)  The Superintendent has a budget of $800,000, raised through local taxes, to allocate between the two activities.

The State Legislature is considering ways to induce XY County to purchase more units of remedial education for underachieving students. It is specifically considering various forms of grants.

1. Budget Constraints:

a. Draw and label Superintendent’s budget line with no State aid (Make sure to put units of remedial instruction on the horizontal axis)

b. Assume the Superintendent chooses to purchase 100 units of remedial instruction and 600 of “other school activities. Label this is allocation as point “K” on your diagram

2. Open-Ended Matching Grants:

a. One option for the State is an open-ended matching grant, under which the state would match XY School District one-for-one every dollar the District spends on remedial instruction. Draw and label the superintendent’s new budget constraint under this program (you should draw this new budget line on the same graph you produced in #1 above)

3. Close-End Matching Grants:

a. A legislator, fearing school districts will respond so aggressively to the subsidy for remedial instruction provided by the matching grant that it will be too costly, proposes that the matching grant program be closed-ended, such that no district can receive more than $100,000 of state aid.  Draw and label the Superintendent’s budget constraint under this closed-end matching grant program (You should draw a new budget line, using the same chart from #1 and #2 above)

b. As a legislator interested in increasing remedial education services, do you think making the matching grant closed ended will lead XY County to provide fewer units of remedial education than if the matching grant were open ended?  Explain.  (Hint, think about income and substitution effects).

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