Question

Consumers in Georgia pay twice as much for avocados as they do for peaches. However, avocados and peaches are the same price in California. If consumers in both states maximize utility, will the marginal rate of substitution of peaches for avocados be the same for consumers in both states? If not, which will be higher?

Short answer

No, the marginal rate of substitution of peaches for avocados will not be the same in both states. It will be higher in Georgia, where the price of avocados is twice as much as peaches, compared to California, where the prices are equal.

Step-by-step solution

Understanding MRS and price ratios

Firstly, it's important to understand the concept of MRS. The marginal rate of substitution (MRS) refers to the rate at which a consumer is willing to exchange one product for another while maintaining the same level of satisfaction or utility. It represents the consumer’s willingness to trade between two goods and is based upon their personal preference. It can be defined as MRS = -MU1/MU2, where MU1 and MU2 are the marginal utilities of goods 1 and 2 respectively. However, it's also crucial to consider the price ratio. In a state of equilibrium (i.e., when a consumer is maximizing utility), the ratio of the prices of the two goods should be equal to the MRS. In this case, the price of avocados to peaches is 2:1 in Georgia and 1:1 in California.

Analysing Georgia Scenario

In Georgia, given that the price of avocados is twice that of peaches, the consumers there must value avocados twice as much as they do peaches. This is because to maximize utility, the MRS should be equal to the price ratio. Therefore, the MRS of peaches for avocados is 2 in Georgia.

Analysing California Scenario

In California, avocados and peaches are the same price. Therefore, consumers in California will have an MRS of 1, showing that they value peaches and avocados equally to maintain utility.

Comparison and Conclusion

By comparing the MRS in both states, it is clear that the MRS in Georgia is higher than in California. This makes sense logically as well, since the price of avocados is higher in Georgia, the consumers there place a higher value on avocados as compared to peaches. Therefore, the consumers in Georgia are willing to give up more peaches to obtain one additional avocado.