Question

# 1. Tim gets utility from only two goods, rice (R) and beans (B). His preferences are...

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

(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.

#### Earn Coins

Coins can be redeemed for fabulous gifts.