Question

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.

Answer 1

U = RB²

(a)

MUR = U/R = B²

MUB = U/B = 2BR

MRS = MUR/MUB = (B²) / (2BR) = B / (2R)

(b)

Budget constraint: M = R x Rp + B x Bp

10,000 = R x Rp + B x Bp

(c)

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]

(d)

Demand function for Rice is independent of price of B, so R & B are neither substitutes nor complements.