Question

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, so MU_s=2T and MU_T = 2S. 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. (Hint: See Q&A 4.3.) 

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. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line.

Answer 1

[What is her marginal utility from shoes and what is her marginal utility from dancing?]

U(S,T) = 2 ST

MUs = 2T
MUt = 2S

[a. What is the equation for Linda's budget line? Draw it (with T on the vertical axis), and label the slopes and intercepts.]

Budget line: 50S + 50T = 500

T = 10 - S

The slope is -1

[b. What is her marginal rate of substitution? Explain.]

MRS = MUs/MUt

MRS = 2T/2S

MRS = T/S

[c. Solve mathematically for her optimal bundle. Show in a diagram how to determine this bundle using indifference curves and a budget line.]

T = S

50S + 50T = 500

50S + 50S = 500

S = 500/100

S = 5

T = 5

Answer 2