Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S,T) = 2 ST. What is her marginal utility from shoes and what is her marginal utility from dancing? It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on clothing and dancing.
a. What is the equation for Linda's budget line? Draw it (with T on the vertical axis), and label the slopes and intercepts.
b. What is her marginal rate of substitution? Explain.
c. Solve mathematically for her optimal bundle. Show in a diagram how to determine this bundle using indifference curves and a budget line.