Denver Bluff High School has $60,000 to spend on computers and other goods so its budget equation is C + X = 60,000, there C is expenditure on computers and X is expenditure on other things. The high school's preferences can be represented by the utility function U(C, X) = CX2, where the marginal rate of substitution is -X/2C. Currently, the high school's optimal bundle is $20,000 of computers, and $40,000 of everything else. a. Graph the school's budget line, with computers on the x-axis and all other goods on the y-axis. Label intercepts and the current optimal bundle and sketch an indifference curve. The State Education Commission wants to encourage "computer literacy" inschools, and so has proposed the following plan: Provide the schools with a "matching grant," in which the state will cover $0.50 of every $1 the school spends on computers (effectively lowering the price of 1 unit of C to $0.50). b. If the state adopts the plan, write the equation for Denver Bluff High's budget constraint. What is the school's optimal bundle (C.X) under this plan?
Denver Bluff High School has $60,000 to spend on computers and other goods so its budget equation is C + X = 60,000, there C is expenditure on computers and X is expenditure on other things. The high school's preferences can be represented by the utility function U(C, X) = CX2, where the marginal rate of substitution is -X/2C. Currently, the high school's optimal bundle is $20,000 of computers, and $40,000 of everything else. a. Graph the school's budget line, with computers on the x-axis and all other goods on the y-axis. Label intercepts and the current optimal bundle and sketch an indifference curve. The State Education Commission wants to encourage "computer literacy" inschools, and so has proposed the following plan: Provide the schools with a "matching grant," in which the state will cover $0.50 of every $1 the school spends on computers (effectively lowering the price of 1 unit of C to $0.50). b. If the state adopts the plan, write the equation for Denver Bluff High's budget constraint. What is the school's optimal bundle (C.X) under this plan?
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 5SQ
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Need to know the new budget constraint equation for part B and the new optimal bundle ([$30k, $40k], right?). See the RED text.
Transcribed Image Text:Denver Bluff High School has $60,000 to spend on computers and other goods so its budget
equation is C + X = 60,000, there C is expenditure on computers and X is expenditure on other
things. The high school's preferences can be represented by the utility function U(C, X) = CX?,
where the marginal rate of substitution is -X/2C. Currently, the high school's optimal bundle is
$20,000 of computers, and $40,000 of everything else.
a. Graph the school's budget line, with computers on the x-axis and all other goods
on the y-axis. Label intercepts and the current optimal bundle and sketch an
indifference curve.
The State Education Commission wants to encourage "computer literacy" inschools, and so has
proposed the following plan: Provide the schools with a "matching grant," in which the state will
cover $0.50 of every $1 the school spends on computers (effectively lowering the price of 1 unit of C
to $0.50).
b. If the state adopts the plan, write the equation for Denver Bluff High's budget
constraint. What is the school's optimal bundle (CX) under this plan?
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