Nicole's income is $1,000 per month. She spends all of it on shoes (S) and books (B). Shoes cost $50 and books cost $25. Her marginal rate of substitution for shoes with books is MRSSB = 2B/3S. Illustrate her utility-maximizing combination of shoes and books and draw her price-consumption curve if the price of books rises to $30.
What will be an ideal response?
At the utility-maximizing combination of shoes and books, MRSSB = 2B/3S = PS/PB = $50/$25, which implies that B = 3S. Substituting this into the budget constraint yields $50S + $75S = $1,000. Solving this equation gives S = 8. Since B = 3S, B = 24. Her initial utility-maximizing combination of shoes and books is represented by point a in Figure 5.13.
To find the price-consumption curve, start with the utility-maximizing condition and solve for S. 2B/3S = PS/PB, which implies that S = (2/3)(PB/PS)B. Substitute this into the budget constraint and solve for B. M = PS (2/3)(PB/PS)B + PBB, which implies B = (3/5) (M/PB ) = B. When PB = $30, B = 20. The new utility-maximizing combination of books and shoes is represented by point b in Figure 5.13. Connecting points a and b gives the price-consumption curve.
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