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# Waste Collectors and Washer Repairfolk

MICRO-LSTFAE

Wesley is the President of the Waste Collector and Washer Repairfolk Technical School, which trains waste collectors and washer repairfolk. He must decide how to distribute revenue between the two programs.

His social welfare function is $U(C,R) = \sqrt{C} + \sqrt{R}$, where $C$ is the number of dollars the waste collector program gets and $R$ is the number of dollars the washer repairfolk get. Wesley has $\$100$to distribute between the two. How much does he give each program? (it might be helpful to think of Wesley’s social welfare function as his utility function, the \$100 as his budget, and the “price” of transferring income from one program to another as \$1) Let’s say that the waste collector program is a bit more wasteful, so it only receives \$1 of funding for every \$2 Wesley spends on it. How much does he give each program now? (think about how Wesley’s budget constraint changes now that the waste collector program is wasteful, and the “price” of giving the waste collectors \$1 is now \$2) If Wesley’s social welfare function changes to$U(C,R) = log C + log R$, how does he distribute funds? For simplicity, we'll go back to assuming the waste collector program is NOT wasteful ("price" is$1 for each program)