Question

Kim has $10 to buy flour and GI Joe's. A bag of flour is $.50 and a GI Joe is $2. If the expected utility of x1x1 bags of flour and x2x2 GI Joes is U(x1,x2)=x21+x22−−−−−−√U(x1,x2)=x12+x22, what point along the budget curve maximized utility? Sol: Find the point where the tangent line is the budget line.

A sample problem would look like: Kim has $10 to buy flour and GI Joe's. A bag of flour is $.50 and a GI Joe is $2. If the expected utility of xy bags of flour and 22 GI Joes is U(21, 22) = x} + xạ, what point along the budget curve maximized utility? Sol: Find the point where tangent line to is the budget line.

Answer 1

Answer :

x_{​​​​​​1} = 20

x_{​​​​​​2} = 0

Budget curve: 0.5x_{​​​​​1} + 2x₂ = 10

​​​​​​The given utility function has indifference curve that is concave. In this case, the utility is maximized at one of the corner points (not at the tangency of indifference curve and budget line).

Here, the price of a bag of flour is lesser than a GI Joe. So, Kim will consume only flour.

So, she will buy bags of flour with all her income.

Therefore, the point where she consumes only flour is the utility maximizing point.

(x_{​​​​​​1}​​​​​, x_{​​​​​​2}) = (20,0)