Question
6. Assume that an individual is rational consumer Who consume anly two goods of Banana (B) and nuts (N) Assum that his marginal hate of a substit tution banana far nuts is given by the Following Formula [ m_(R_(1) s)=(m_(u a))/(m_(B))=(B)/(N) ( That siply equal to the ) ] ratio of the aumber of Banana consumed for the Number af nuts consumes Assume that his income in Birr 200 the price or nuts is Birr 5 and price or bananas is Birr lo what a vantities of Bananas and avits will be consured.
Solution
4.6
(392 Votos)
Luiza
Avançado · Tutor por 1 anos
Resposta
To determine the quantities of bananas and nuts that a rational consumer will consume, we need to consider the consumer's budget constraint and their marginal rate of substitution (MRS).### Given:- **Price of bananas (
)**: Birr 10- **Price of nuts (
)**: Birr 5- **Income**: Birr
- **Marginal Rate of Substitution (MRS)**:
### Budget Constraint:The consumer's budget constraint can be expressed as:
### Optimal Consumption:A rational consumer maximizes utility by consuming goods such that the MRS equals the price ratio. Therefore, the condition for optimal consumption is:
Substituting the given MRS and prices:
This implies:
### Solving the System of Equations:Now, substitute
into the budget constraint:
Using
:
### Conclusion:The quantities of bananas and nuts consumed are:- **Bananas (
)**:
- **Nuts (
)**:
These expressions give the quantities in terms of income
. To find specific quantities, you would need to know the exact value of
.