1. Suppose that Jana cares only about apples and lettuce. Her utility function is **U = A**^{0.5}**L**^{0.5}**,** where A is the number of apples and L is the number of heads of lettuce that she consumes. The price of apples is $1, and the price of lettuce is $4. Suppose that Jana have $40 to spend.

a) Determine the maximum number of apples (A) and heads of lettuce (L) she can purchase if she only purchase apples or only purchases lettuce. 2 points

b) State Jana's budget constraint (line) in the format L= intercept - slope * A 1 point

c) Determine Jana's MRS_{AL (Apples for Lettuce)} 1 point

d) Does Jana's utility function satisfy the rules "*more is better*" and "*diminishing marginal utility"*? Motivate your answers. 2 points

e) What is the optimal number of apples (A) and heads of lettuce (L) for Jana given her budget constraint? 2 points

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