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Suppose that Maggie cares only about chai and bagels

Economics

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Suppose that Maggie cares only about chai and bagels. Her utility function is U= CB, where C is the number of cups of chai she drinks in a day, and B is the number of bagels she eats in a day. The price of chai is $3, and the price of bagels is $1.50. Maggie has $6 to spend per day on chai and bagels.

1. State the objective function
2. State the constraint
3. Solve for MU_C and MU_B and state if utility function exhibits diminishing MU for each good
4. Interpret the value of your MU_C and MU_B at C=2 and B=6
5. Solve for MRS_CB and state if the utility function exhibits diminishing MRS
6. Interpret the value of your MRS_CB if P=2 and S=1
7. Write down the optimality condition. Express it using the utility function and prices given above.
8. What is the economic meaning of the optimality condition applied specifically to the chai and bagels. Equality of slopes of IC and BL are not acceptable answers- these are not economically relevant terms
9. Solve for optimal level of chai and bagels.
10. Draw your optimal solution by drawing an IC (convex one) and BL, and make sure you label your optimal levels of B and C as well as the intercepts of your BL