Remember Bonnie and Clyde from your workbook? Suppose that their total profits are 40H, where H is the number of hours they work per year.Their utility functions are, respectively,
U_B(C_B, H ) = C_B - 0.02H ² and U_C(C_C, H ) = C_C - 0.03H ², 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 must be

Question

Quizplus · Accepted Answer

To find the Pareto optimal choice, we need to set up the following conditions: 1. Both Bonnie and Clyde need to be on their indifference curves (i.e. maximizing their utility) 2. Total profits need to be maximized Let's start with Bonnie's utility function: U_B(C_B, H )F1F1F1S1F1F1F10 C_B F1F1F1S1F1F1F10 0.02H ² To find the optimal hours of work, we need to take the partial derivative of her utility function with respect to H: 0.02 - 0.02(C_B)/H Setting this equal to zero and solving for H, we get: C_B = 50H Now let's look at Clyde's utility function: U_C(C_C, H )F1F1F1S1F1F1F10 C_C F1F1F1S1F1F1F10 0.03H ² To find the optimal hours of work, we need to take the partial derivative of his utility function with respect to H: 0.03 - 0.03(C_C)/H Setting this equal to zero and solving for H, we get: C_C = 33.33H Now we can use the total profits function to find the income distribution between Bonnie and Clyde: 40H = C_B + C_C Substituting in the optimal values for C_B and C_C, we get: 40H = 50H + 33.33H H = 150 Therefore, the optimal number of hours Bonnie and Clyde should work per year to achieve a Pareto optimal choice of hours and income distribution is 150.

Remember Bonnie and Clyde from Your Workbook? Suppose That Their