Answer to Question #50985 in Microeconomics for alishia

Question

Karina 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 so MUs =2T and MUt =2S

It cost Karina N$50 to buy a new pair of shoes or to spend an evening out dancing.Assume that she has N$500 to spend on clothing and dancing.

a)Show the equation for Karina's budget line and draw the budget line with T on the vertical axis (label the slope and intercepts)

b)What is Karina's marginal rate of substitution (MRS)?Explain

c)Solve mathematically for Karina's optimal bundle.

d)Show how to determine this bundle in a diagram using indifference curves and budget line

Answer 1

U(S,T)=2ST, so MUs =2T and MUt =2S, 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 = 2T/2S = T/S
c) Her optimal bundle is in the point of intersection of budget line and indifference curve. In our case, as MRS = T/S, 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.