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

Expert's answer

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.

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.

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