Question

You are given the Cobb-Douglas utility function:

u = a₁^a * b
and the budget equation:
y = p₁q₁ + p₂q₂
Complete the following:
(a) Derive the ordinary demand function based on this utility function and budget equation.

Answer 1

To derive the ordinary demand function, we can substitute the budget equation into the utility function and solve for the utility-maximising quantity of q₁.

Step-by-step explanation:

To derive the ordinary demand function in this scenario, we need to maximize the utility function subject to the budget constraint. We can start by rewriting the budget equation as follows: y = P₁q₁ + P₂q₂ = income. Since we want to find the demand function for q₁, we can solve for q₂ in terms of q₁: q₂ = (income - P₁q₁) / P₂. Next, we substitute the value of q₂ into the utility function, giving us
`u = a₁^a * b(a₂ - P₁q₁) / P₂`. We differentiate the utility function with respect to q₁ and set it equal to zero to find the utility-maximising quantity of q₁. Solving this equation will derive the ordinary demand function for q₁ in terms of the given parameters.