Question

In: Economics

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 XR . X2B = 64, where XR and XB 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.

2.

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

Here,

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

3.

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
Next > < Previous

Related Solutions

Suppose that Tim gets utility from only two goods, rice (R) and beans (B) and his...
Suppose that Tim gets utility from only two goods, rice (R) and beans (B) and his preferences are represented by the utility function U(R,B) = R^2 * B^5. If Tim's income is 42 and price of rice is 1, price of beans is 3. How many units of rice and beans will he choose? Tim’s income elasticity of demand for beans? Explain clearly plz.
Consider the utility function of a consumer who obtains utility from consuming only two goods, ?1...
Consider the utility function of a consumer who obtains utility from consuming only two goods, ?1 and ?2 , in fixed proportions. Specifically, the utility of the consumer requires the consumption of two units of ?2 for each unit of ?1. i. Report the mathematical expression of the utility function of the consumer. ii. Provide a diagram of the corresponding indifference curves. iii. Provide at least one example and economic intuition. Suppose that the consumer has available income equal to...
Consider the utility function of a consumer who obtains utility from consuming only two goods, ?1...
Consider the utility function of a consumer who obtains utility from consuming only two goods, ?1 and ?2 , in fixed proportions. Specifically, the utility of the consumer requires the consumption of two units of ?2 for each unit of ?1. A. i. Report the mathematical expression of the utility function of the consumer. ii. Provide a diagram of the corresponding indifference curves. iii. Provide at least one example and economic intuition. Suppose that the consumer has available income equal...
A consumer spends all of his income only on two goods, X and Y. His utility...
A consumer spends all of his income only on two goods, X and Y. His utility function is given by U=XY. The price of good X is $P and the price of good Y is $2. His income is $400. (4) Derive the PCC (price consumption curve) of this consumer as the price of good X changes . (3) Derive this consumer’s demand function for good X. (3) As the price of good X falls, this consumer’s demand becomes less...
A consumer spends all of his income only on two goods, X and Y. His utility...
A consumer spends all of his income only on two goods, X and Y. His utility function is given by U=XY. The price of good X is $P and the price of good Y is $2. His income is $400. Derive the PCC (price consumption curve) of this consumer as the price of good X changes . Derive this consumer’s demand function for good X. As the price of good X falls, this consumer’s demand becomes less elastic. True or...
Ana gets utility from Pepperoni sticks and Tea. Ana enjoys variety across the two goods. Her...
Ana gets utility from Pepperoni sticks and Tea. Ana enjoys variety across the two goods. Her dog, Lexie, gets utility only from Pepperoni sticks. (a) [5 points] With P on the x-axis and T on the y-axis, draw some representative indifference curves for Ana. In a separate but identically labeled diagram, draw some representative indifference curves for Lexie. Identify the direction of increasing utility. (b) [15 points] Assume Ana is endowed with 10 P and 5 T and Lexie is...
1.     Elmer is updating his summer wardrobe.  The amount of utility he gets from shirts and shorts is...
1.     Elmer is updating his summer wardrobe.  The amount of utility he gets from shirts and shorts is listed in the table below, where each number represents how much utility (in utils) he receives from the combination of shirts and shorts. 1 shirt 2 shirts 3 shirts 4 shirts 1 pair of shorts 15 27 37 46 2 pairs of shorts 26 37 45 51 3 pairs of shorts 35 45 51 55         a.     What is the marginal utility from buying another pair...
11. A consumer’s utility only depends on the consumption of goods A and B according to...
11. A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A^(1/3)B^(2/3). The price of goods A and B are $30 and $45, respectively. The consumer has a budget of $2700 that he can use to consume the two goods. Question a) A new tax of 6% is imposed on the price of good B. Compute the new optimal bundle of good A and B for the...
1) Ben allocates his snack budget between two goods, chocolate and fruit. Write down his utility...
1) Ben allocates his snack budget between two goods, chocolate and fruit. Write down his utility function and the equation of his budget line. What is the slope of his budget line, if chocolate is on the horizontal axis? If he uses all of his snack budget on chocolate, what is the maximum amount of chocolate he could purchase?
Tim has a concave utility function u(w) = w ‐ w²/2, where w∈[0,1] His only major...
Tim has a concave utility function u(w) = w ‐ w²/2, where w∈[0,1] His only major asset is shares in an Internet start‐up company. Tomorrow he will learn his stock's value. He believes that it is worth $w0 with probability 4/5 and $w1 with probability 1/5, with w1 > w0.   1) Calculate the expected value of the lottery, the expected utility, and the utility of the expected value. 2) If w0 = 1/3 and w1 = 2/3. Compute the risk...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT