On Friday Sam goes to the market to buy apples and donuts. Suppose Sam has a utility function for apples and donuts with the following form: U(S)(A,D)=A((1)/(3))D((3)/(3)) where D represents a donut and A represents an apple.
i. Suppose a donut costs 0.60 and an apple cost 0.90. How many apples and donuts will Sam purchase in order to maximize her utility if she has 10.80 to spend?
ii. Draw a graph that displays this maximum.
iii. Use this example to explain the Optimization Principal in relation to income constrained utility maximization. Suppose that Sam goes fishing on a small boat with Frodo on Saturday. Frodo brings 4 donuts and 6 apples, while Sam brings all of the apples and donuts that she purchased on Friday. While on the boat they can exchange and consume the apples and donuts, but they will not be able to purchase additional food. Suppose that Frodo has a utility function for apples and donuts with the following form: UF(A,D) = 3A + 2D.
iv. Draw an Edgeworth Box that presents this exchange economy. Clearly label all axis, and the original allocation.
v. Define a pareto optimal allocation.
vi. Calculate and define the set of Pareto Optimal allocations for this exchange economy.
vii. Show on the graph the set of Pareto Optimal allocations and the Core of this exchange economy.
