You are given the following shortrun production function x

You are given the following short-run production function: x = f(v) = 4v + 0.12v^2 - 0.0002v^3. Over what range of inputs does this production technology exhibit increasing marginal returns? 0 to 200 Over what range of inputs does this production technology exhibit diminishing marginal returns? 200 to -416 What is the maximum level of output that this production technology can achieve? 4/6 At what level of output do marginal costs begin to rile? 4,000 Use the information you have generated in parts (a) to (c) to modify the diagrams below by adding the total product, marginal product, and average product curves with appropriate curvature properties.

Solution

a)

Calculate the first order condition.

This comes out to be: 4+0.24v-0.0006v^2

For all those values of v when the derivative is greater than 0, there are increasing returns to scale.

b)

Calculate the first order condition.

This comes out to be: 4+0.24v-0.0006v^2

For all those values of v when the derivative is less than 0, there are diminishing returns to scale.

c)

Calculate the first order condition.

This comes out to be: 4+0.24v-0.0006v^2

Find the value of v when the derivative is equal to 0, tihs is the maximum level.

d)

This occurs at the point df/dv curve starts to fall.