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)=2ST. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that he has $500 to spend on clothing and dancing.
a) What is the equation for her budget line? Draw it (with T on the vertical axis), and label the slope and intercepts.
b) What is Linda’s marginal rate of substitution? Explain.
c) Solve mathematically for her optimal bundle.
d) Show how to determine this bundle in a
diagram using indifference curves and a budget line.
U(S,T)=2ST, Pt = PS = $50, B = $500. a) The equation for her budget line is: Pt*T + PS*S = B 50T + 50S = 500 b) The marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility. Linda’s marginal rate of substitution is MRS = MUs/MUt = 2/2 = 1 c) Her optimal bundle is in the point of intersection of budget line and indifference curve. In our case, as MRS = 1, so at this point S = T, so 50T + 50T = 500 and T = S = 5 units. d) To determine this bundle graphically, we should find the point (or points), where the budget line intersects with indifference curves.