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# Answer to Question #50985 in Microeconomics for alishia

Question #50985
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
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&nbsp;marginal rate of substitution&nbsp;is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining&nbsp;the same level of&nbsp;utility.&nbsp;Linda&rsquo;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&nbsp;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.

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