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4. Erin and Sarah are business partners. Whenever they work they have to work together. Their only source of income is the income from their partnership. Total profits per year are 50H where H is the number of hours they work per year. (H must be the same for both Erin and Sarah since they always work together. Thus H is a public good in this case.) Sarahs utility function is Us(Cs, H) Cs 02H2 where Cs is the amount of money spent on consumption each year, and Erins utility function is UE(CE, H)CE - .005H2, where Ce is Erins consumption measured in dollars (a) What is Sarahs MRS between the private and public goods (i.e., what is the ratio of her marginal utility of the public good to her marginal utility of the private good)? (b) Answer (a) for Erin. c) Write an expression for the sum of their marginal rates of substitution. (d) What is the Pareto optimal number of hours to work?

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