Recall Bonnie and Clyde from Problem 5. Suppose that their total profits are 256H, where H is the number of hours they work per year. Their utility functions are, respectively, U_B(C_B, H) = C_B - 0.04H² and U_C(C_C, H) = C_C - 0.04H², where C_B and C_C are their private goods consumptions and H is the number of hours they work per year. If they find a Pareto optimal choice of hours of work and income distribution, the number of hours they work per year is

Question

Quizplus · Accepted Answer

To find the Pareto optimal number of hours, we maximize the sum of their utilities subject to the constraint that their total consumption equals their total profits. The utility functions are quadratic in H, and the profit function is linear in H. Solving for the optimal H involves setting the derivative of the sum of utilities with respect to H equal to zero, which yields H = 1,600.