Question

Find the marginal product of each input, determine if the production function has diminishing marginal product for each input, determine if the production function has constant, increasing, or decreasing returns-to-scale. f(x, y) = min{12x, 3y}.

Answer 1

Q = f(x, y) = min{12x, 3y}

Marginal product of x, MPx = dQ/dx = 12
Thus, MPx is constant and not diminishing because it is a constant value.

Marginal product of y, MPy = dQ/dy = 3
Thus, MPy is constant and not diminishing because it is a constant value.

Now, let x = tx and y = ty where t is a constant and t > 1.
So, Q' = f(tx, ty) = min{12tx, 3ty} = min{t(12x, 3y)} = tmin{12x, 3y} = tQ
Thus, we can see that power of t is 1 which means that there are constant returns to scale.