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.

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).<br /><br />### Given:<br />- **Price of bananas (\(P_B\))**: Birr 10<br />- **Price of nuts (\(P_N\))**: Birr 5<br />- **Income**: Birr \(I\)<br />- **Marginal Rate of Substitution (MRS)**: \(\frac{B}{N}\)<br /><br />### Budget Constraint:<br />The consumer's budget constraint can be expressed as:<br />\[ P_B \times B + P_N \times N = I \]<br />\[ 10B + 5N = I \]<br /><br />### Optimal Consumption:<br />A rational consumer maximizes utility by consuming goods such that the MRS equals the price ratio. Therefore, the condition for optimal consumption is:<br />\[ \text{MRS} = \frac{P_B}{P_N} \]<br /><br />Substituting the given MRS and prices:<br />\[ \frac{B}{N} = \frac{10}{5} \]<br />\[ \frac{B}{N} = 2 \]<br /><br />This implies:<br />\[ B = 2N \]<br /><br />### Solving the System of Equations:<br />Now, substitute \(B = 2N\) into the budget constraint:<br />\[ 10(2N) + 5N = I \]<br />\[ 20N + 5N = I \]<br />\[ 25N = I \]<br />\[ N = \frac{I}{25} \]<br /><br />Using \(B = 2N\):<br />\[ B = 2 \left(\frac{I}{25}\right) = \frac{2I}{25} \]<br /><br />### Conclusion:<br />The quantities of bananas and nuts consumed are:<br />- **Bananas (\(B\))**: \(\frac{2I}{25}\)<br />- **Nuts (\(N\))**: \(\frac{I}{25}\)<br /><br />These expressions give the quantities in terms of income \(I\). To find specific quantities, you would need to know the exact value of \(I\).