Question

The utility function is u = Q^0.3Q^0.7 for beef and pork. bp

(a) What is the marginal utility of beef? [MUb = ∂U/∂Qp] What is the marginal utility of ork? [MUp =∂U/∂Qb ]

Answer 1

The marginal utility of beef (MUb) and pork (MUp) are derived from the utility function by taking the partial derivatives, resulting in MUb = 0.3 × Qb-0.7Qp0.7 and MUp = 0.7 × Qb0.3Qp-0.3.

Step-by-step explanation:

The marginal utility of beef can be found by taking the partial derivative of the utility function with respect to the quantity of beef (Qb), and the marginal utility of pork can be found by taking the partial derivative with respect to the quantity of pork (Qp). Given the utility function u = Qb0.3Qp0.7, let's find the marginal utilities.

The marginal utility of beef (MUb) is calculated as:

MUb = ∂U/∂Qb = 0.3 × Qb-0.7Qp0.7

The marginal utility of pork (MUp) is calculated as:

MUp = ∂U/∂Qp = 0.7 × Qb0.3Qp-0.3

In both cases, we are applying the power rule for differentiation to find the partial derivative. This calculation is essential for understanding how the satisfaction or utility changes with the consumption of an additional unit of beef or pork.