Question: suppose there are only two goods in the world apples...
- 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)
- 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).
- What is the slope of the budget line?
- What is the slope of the indifference curve (MRS)?
- Write the intuition behind the MRS (in terms of the substitutability of apples and oranges)
- 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)