Connetquot High School, where I went to school (Go T-birds!) has $60,000 to spend on computers (C) and other stuff (Y), so its budget equation is given by C + Y =60,000, where C is expenditure on computers and Y is expenditures on other stuff. C.H.S. currently plans to spend $20,000 on computers and $40,000 on other things. The state wants to encourage computer literacy in all high. The following two plans have been proposed.
Plan A: Give a grant of $10,000 to each high school in the state that the school could spend as it wished.
Plan B: A "matching grant." For every dollar's worth of computers that a high school orders, the state will give the school 50 cents.
a.) Suppose that the headmaster's preferences for expenditures on computers and other things are given by the utility function U=C0.5*Y. Calculate how much the headmaster will choose to spend on computers and other goods if it does not adopt any plan, under Plan A, and Plan B.
b.) Which would the headmaster prefer: No plan, Plan A or Plan B? Explain