1. Tim gets utility from only two goods, rice (R) and beans (B). His preferences are represented by the utility function U(R,B) = R x B^2
a. Compute Tim’s marginal rate of substitution, as a function of R and B.
b. Suppose Tim’s income is 10000 and the prices of rice and beans are R p and B p (both > 0). Write Tim’s budget constraint.
c. Compute Tim’s demand function for rice.
d. For Tim, are rice and beans complements, substitutes, or neither? Explain your answer.
U = RB2
MUR = U/R = B2
MUB = U/B = 2BR
MRS = MUR/MUB = (B2) / (2BR) = B / (2R)
Budget constraint: M = R x Rp + B x Bp
10,000 = R x Rp + B x Bp
Utility is maximized when MRS = Rp / Bp
B / 2R = Rp / Bp
B x Bp = 2R x Rp
Plugging in budget line,
M = R x Rp + 2R x Rp
M = 3R x Rp
R = M / (3Rp) [demand function for Rice]
Demand function for Rice is independent of price of B, so R & B are neither substitutes nor complements.
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