1. Tim gets utility from only two goods, rice (R) and beans (B). One of his...

1. Tim gets utility from only two goods, rice (R) and beans (B). One of his indifference curves is given by the formula X_R . X²_B = 64, where X_R and X_B are the quantities of rice and beans.

a. Give two examples of bundles that lie on this indifference curve, with whole-number quantities of both goods.

b. Suppose Tim currently has a bundle on this indifference curve, with 2 units of beans. Use derivatives to calculate the rate at which he is willing to exchange beans for rice. (That is, how many units of rice would he need to receive in exchange for one unit of beans?)

c. If Tim were to give up a unit of beans, how many units of rice would he have to receive in order to stay on the same indifference curve (i.e., to remain equally well off)? Why is the answer different from that in (b)?

Solutions

Expert Solution

1. Indifference Curve is given by the equation

Examples of bundles lying on the above indifference curve: (1,8), (4,4)

These can be verified by plugging in the values of and to the given indifference curve.

Plugging the value of in the given indifference curve, we get

The rate at which Tim is willing to exchange beans for rice is given by his Marginal Rate of Substitution

$MU_B=2X_RX_B,{_}MU_R=X_B^2$

Here,

Hence, Tim would need 16 units of rice in exchange for 1 unit of beans.

To remain at 64 units of satisfaction, we solve the equation

Hence, Tim would have to receive 64 - 16 = 48 units of rice to remain on the same indifference curve offering him a satisfaction of 64 units.

The MRS is the rate at which Tim is willing to exchange one unit of beans for rice. Here, we found the units of rice Tim would need in order to stay on the same indifference curve if a unit of beans was given up by Tim. Hence, the two answers are different.

Rahul Sunny answered 1 year ago

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