A firm uses 3 factors to produce its output.Its production function is f(x, y, z)= min{x³/y, y², (z⁴ - x⁴)/y²}.If the amount of each input is multiplied by 3, its output will be multiplied by A)0.30. B)3. C)9. D)27. E)The answer depends on the original choice of x, y, and z.

Question

Quizplus · Accepted Answer

According to the Cobb-Douglas production function, the output is a function of the inputs raised to a power, where the exponents are the elasticities of production with respect to each input. In this case, the production function is: f(x,y,z) = (x/y)^1/3 * y^1/3 * (z/(x/y))^1/3 = x^1/3 * y^1/3 * z^1/3.

If each input is multiplied by 3, the new production function will be: f(3x,3y,3z) = (3x/(3y))^1/3 * (3y)^1/3 * (3z/(3x/3y))^1/3 = x^1/3 * y^1/3 * z^1/3 * 3^(1/3) * 3^(1/3) * 3^(1/3) = 3 * f(x,y,z). Therefore, the output will be multiplied by 9 (option C).

A Firm Uses 3 Factors to Produce Its Output