Question: Charlie likes both apples and bananas. He consumes nothing else. Charlie consumes \(x_{1}\) bushels of apples per year and \(x_{2}\) bushels of bananas per year. Suppose that Charlie's preference is represented in the following utility function: \(\left(x_{1} x_{2}\right)=x_{1} x_{2} .\) Also, suppose that the price of \(x_{1}\) is $1, the price of \(x_{2}\) is $2, and Charlie's income is $40.

1. Express the function of budget constraint for Charlie.
2. What is the marginal utility for the apples? What is the marginal utility for the bananas? (3 points)
3. Using marginal utilities, find Charlie's marginal rate of substitution.
4. What is the slope of Charlie's budget line? Using this and the answer to (c), write an equation, which implies the optimal choice: an equation that implies that the budget line is tangent to an indifference curve.
5. Find the optimal consumption choice bundle \(\left(x_{1}, x_{2}\right) .\)
6. Using the answer to (e), find Charlie's total utility if he consumes the optimal consumption bundle.

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document