Question

In: Economics

Consider the following 2 good, 2 consumers, one producer world. Moe, the producer, makes Soda (S)...

Consider the following 2 good, 2 consumers, one producer world. Moe, the producer, makes Soda (S) and Moon Pies (P). Homer (H) is one consumer. Barney (B) is the other. (Moe ate at home so he is not a consumer for this one.) There are no externalities involved in the consumption of either good. Everyone, including Moe, acts competively. Homer and Barney have placed their orders, but there is still time to change them. Money can be used for nothing other than to purchase soda or moon pies. Currently, the situation is such that, if each person eats what’s on his respective order, their marginal utilities are as follows:

MU (Homer-Soda)= 60

MU (Homer-Moon Pies) = 45

MU (Barney –Soda) = 24

MU (Barney-Moon Pies) = 18

MC (Soda) = $2.00

MC (Moon Pies) = $1.50

a. What is each person’s Marginal Rate of Substitution?

b. What is the producer’s (Moe’s) Marginal Rate of Transformation (MRT)?

c. Is the current situation allocatively efficient? Explain why this is. If there is not enough information to answer this situation, tell me what missing information you need and why you need it.

d. Is this situation (pareto) efficient when we consider Moe’s production costs and his ability to change production? Explain why this is. If there is not enough information to answer this situation, tell me what missing information you need and why you need it.

Expert Solution

Given two goods which are produced; Soda(S) and Moon pies(M)

a.

Marginal rate of substitution is the rate at which a consumer can give up some quantity of one good in order to consume the other without compromising on its utility.

here, there are two consumers; Homer and Barney

so the marginal rate of substitution numerically is the ratio of the marginal utilities of one good with respectto the other.

for Homer's marginal rate of substitution for soda with respect to moon pies is

implies that Homer is ready to give up 1.3 units of moon pies to get an extra unit of soda.

Similarly for Barney,

Barney is also ready to give up 1.3 units of moon pies to get additional unit of soda.

b.

Marginal rate of transformation or MRT is the rate at which some amount of a good is given up in order to produce another good given the technology remains constant.

MRT for producer Moe , numerically is the ratio of the marginal costs of the two goods.

calculating for MRT of soda with respect to moon pies will be

therefore, Moe will give up production of 1.3 units of moon pies in order to produce an extra unit of soda.

c.

the current allocation might be efficient because one of the conditions required is fulfilled and that is MRS=MRT but it also depends on the market prices of the two goods which are not been given so it requires an additional information about the prices of the goods.

d.

Pareto efficiency requires efficiency in exchange and production which implies that MRT and MRS must be equal to the pride ratio of two goods and then equal to each other in order to be pareto efficient.

hence, it requires the prices of the two goods should be given.

Rahul Sunny answered 2 years ago

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