Mama Mboga in Kiambu works a day and earns an income of 24 Kenya Shillings. At the end of the day she spends all her income to consume only Sukuma wiki (W) and Nyama (N). The satisfaction she gets from this behavior is given by S=2W2+3N3. The price of Sukuma Wiki is 2 shillings while the price of Nyama is 3 shillings. Assume you didn’t know her daily income, what would be the expression for the demand for Nyama? 3 MarksQuestion 13Select one:a.m/6.2b.M/3.4c.M/6d.M/3.3

The question is asking for the expression for the demand for Nyama, given the satisfaction function and the prices of Sukuma Wiki and Nyama.

First, we need to set up the budget constraint. Mama Mboga spends all her income (M) on Sukuma Wiki and Nyama. So, the total cost of Sukuma Wiki and Nyama is equal to her income:

2W + 3N = M

Next, we need to maximize her satisfaction subject to this budget constraint. The satisfaction function is S = 2W^2 + 3N^3.

To do this, we can use the method of Lagrange multipliers. The Lagrangian is:

L = 2W^2 + 3N^3 - λ(2W + 3N - M)

Taking the derivative with respect to W, N, and λ, and setting them equal to zero, gives the following equations:

4W - 2λ = 0 9N^2 - 3λ = 0 2W + 3N - M = 0

Solving these equations simultaneously for W, N, and λ gives the demand functions for Sukuma Wiki and Nyama.

The demand for Nyama (N) is then:

N = (M/3)^(1/2)

So, none of the options a, b, c, or d is correct. The correct answer is (M/3)^(1/2).

The question is asking for the expression for the demand for Nyama, given the satisfaction function and the prices of Sukuma Wiki and Nyama.

First, we need to set up the budget constraint. Mama Mboga spends all her income on Sukuma Wiki and Nyama. Let M be her daily income. Then, the budget constraint is 2W + 3N = M.

Next, we need to maximize her satisfaction subject to this budget constraint. The satisfaction function is S = 2W^2 + 3N^3.

To find the demand for Nyama, we need to take the derivative of the satisfaction function with respect to N, and set it equal to the price ratio (the price of Nyama divided by the price of Sukuma Wiki).

The derivative of the satisfaction function with respect to N is 9N^2. Setting this equal to the price ratio (3/2), we get:

9N^2 = 3/2

Solving for N, we get N = sqrt((3/2)/9) = sqrt(1/6).

Therefore, the demand for Nyama is M times this quantity, or M*sqrt(1/6). This is closest to option c, M/6.

The question is asking for the expression for the demand for Nyama, given the satisfaction function and the prices of Sukuma Wiki and Nyama.

First, we need to set up the utility maximization problem. Mama Mboga wants to maximize her satisfaction subject to her budget constraint.

The satisfaction function is S = 2W^2 + 3N^3.

The budget constraint is M = 2W + 3N, where M is her daily income.

To find the demand function for Nyama, we need to solve this maximization problem.

First, we take the derivative of the satisfaction function with respect to N, which gives us 9N^2.

Then, we take the derivative of the budget constraint with respect to N, which gives us 3.

Setting these two equal to each other gives us 9N^2 = 3, or N^2 = 1/3.

Taking the square root of both sides gives us N = sqrt(1/3), or approximately 0.577.

Therefore, the demand for Nyama is approximately 0.577 times her daily income.

This is not one of the options given in the question, so there may be a mistake in the question or in my calculations.