Clarke County 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 Graphically show 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. %3D b. The State Education Commission wants to encourage "computer literacy" in schools, and so has proposed the following plan: Give a grant of $20,000 to each school in the state, which the school can use only for computers. If the state adopts the plan, add the school's new budget constraint to the graph above, making sure to label the line and the appropriate intercepts. What is the school's optimal bundle (C,X) under this plan?

Clarke County 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 ?(?, ?) = ??2, where the marginal rate of substitution is −?/2?. Currently, the high school’s optimal bundle is $20,000 of computers, and $40,000 of everything else.
a. Graphically show 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.
b. The State Education Commission wants to encourage “computer literacy” in schools, and so has proposed the following plan: Give a grant of $20,000 to each school in the state, which the school can use only for computers. If the state adopts the plan, add the school’s new budget constraint to the graph above, making sure to label the line and the appropriate intercepts. What is the school’s optimal bundle (C,X) under this plan?