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Question: suppose there are only two goods in the world apples...

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  1. Suppose there are only two goods in the world, apples, and oranges. The price of an apple is Pa=2 and the price of an orange is Po=3. Assume there is an individual with the following utility function u = 2xa2 + 0.5xo2  The income available for this individual is l=120 (marginal utility for apples is 4x a and marginal utility for oranges is xo)
    1. Draw the budget line for this individual. Make sure to label the corner points correctly (the points where the budget line touches the x and y axes).
    2. What is the slope of the budget line?
    3. What is the slope of the indifference curve (MRS)?
    4. Write the intuition behind the MRS (in terms of the substitutability of apples and oranges)
    5. What is the utility maximization point? That is, what are the quantities of apples and oranges that maximize the individual’s utility given his budget? (Hint: equate the slope of the budget line with the slope of the indifference curve to get an equation relating xa and x o Use this equation along with the budget line equation to solve for xa and xo)
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