Question

1. ) Using the following production function Y = 12X² - 4X³ to answer the following questions.

1. Find the APP equation.
2. Find the MPP equation.
3. At what level of Y will APP, and MPP reach its maximums (Hint: find X where each equation has the maximum value first)?

Answer 1

We have the following information

Production function: Y = 12X² – 4X³

Average physical product (APP) = Y/X = 12X – 4X²

Marginal physical product (MPP) = ΔY/ΔX = 24X – 12X²

Taking APP first

APP = 12X – 4X²

Taking the first derivative

ΔAPP/ΔX = 12 – 8X = 0

X = 1.5

Taking the second derivative

Δ²APP/ΔX² = – 8

Since, the second derivative is negative so, the APP is maximum when X = 1.5

Now taking MPP

MPP = 24X – 12X²

ΔMPP/ΔX = 24 – 24X = 0

X = 1

Taking the second derivative

Δ²MPP/ΔX² = – 24

Since, the second derivative is negative so, the MPP is maximum when X = 1.