Leah loves buying shoes and going out to dance. Her utility function for pairs of shoes,...

Leah loves buying shoes and going out to dance. Her utility function for pairs of shoes, X, and the number of times she goes dancing per month, Y, is given by

U(x,y)=20XY2+100U(x,y)=20XY2+100

Now suppose that a pair of shoes sells for $10 and it costs Leah $5 to spend an evening out dancing. And assume that she has $90 to spend on clothing and dancing. You are now asked to derive consumer equilibrium.

a. What is the equation for her budget line? Draw it, and find the slope, y-intercept, and x-intercept.

b. Use math to solve for her optimal bundle. Show all works to find an optimal bundle.

c. Show how to determine this bundle in a diagram using indifference curves and a budget line.

d. At an optimal choice, what is the level of utility?

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

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