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 = RB^{2}

(a)

MUR =
U/R
= B^{2}

MUB = U/B = 2BR

MRS = MUR/MUB = (B^{2}) / (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.

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