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

###### Question details

- Suppose there are only two goods in the world, apples, and
oranges. The price of an apple is P
_{a}=2 and the price of an orange is P_{o}=3. Assume there is an individual with the following utility function u = 2x_{a}^{2}+ 0.5x_{o}^{2}The income available for this individual is l=120 (marginal utility for apples is 4x_{a}and marginal utility for oranges is x_{o})- 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 x
_{a}and x_{o}Use this equation along with the budget line equation to solve for x_{a}and x_{o})