Bonnie and Clyde are business partners and whenever they work they have to work together. Its only source of income is this society. Their total annual benefits are 50H, where H is the number of hours they work per year. Since they have to work together, they both have to work the same number of hours, so the variable << work hours >> equals a public <> for the community of two people of Bonnie and Clyde. Bonnie's utility function is U_B C_B H = C_B - 0.02H² and Clyde's utility function is U_C U_C H = Cc - 0.005H², where C_B and C_C represent the annual amounts of money that Bonnie and Clyde employ consumer goods.

(a) If the number of hours they work is H, what is for Bonnie the relationship between the marginal utility of hours of work and the marginal utility of private goods

(b) If Bonnie and Clyde work H hours, then the total amount of money that would be needed to compensate them both for working an additional hour will be equal to the sum of the amount of money needed to compensate Bonnie and the amount it takes to make it up to Clyde. This quantity is roughly equal to the sum of the absolute values of their marginal substitution ratios between labor and money. Develop an expression that allows you to determine this amount based on H. How much additional money will they get if they work an additional hour

(c) illustrate an equation to determine the number of hours of work of Bonnie and Clyde efficient in the sense of Pareto. Determine the value of H efficient in the Pareto sense. Hint: note that this model is formally the same as the model of a public good, H, and a private good, income.