Question

2.1 Consider the production function: Y=2X + 16X2- 0.4X3 a) Derive marginal value product (VMP) and average value product (AVP) equations. [04] b) At what levels of X do the TPP reach its maximum? [03] c) At what level of X does stage two (II) begin or stage one (I) end? [04] d) Find and interpret elasticity of production (EP) when X = 1. [02]

Answer 1

$Y=2X+16X^{2}-1.2X^{3}$

$VMP=\frac{dy}{dx}=2+32X-1.2X^{2}$

$AVP=\frac{Y}{X}=2+16X-0.4X^{2}$

TPP is maximum when $VMP=0$

$2-32X-1.2X^{2}=0$

Solving for X using quadratic formula

$X=\frac{-b+-√(b^{2}-4ac)}{2a}$

$= \frac{-32+-√(32^{2}-4×-1.2×2)}{2×-1.2}=26.7$

Stage 2 begins when$VMP=AVP$

$2-32X-1.2X^{2}=2+16X-0.4X^{2}$

$0-48X-0.8X^{2}$

Solving for X using quadratic formula

$\frac{48+-√(48^{2}-4×-0.8×0)}{2×-0.8}=60$

$EP=\frac{VMP}{AVP}$

$=\frac{2-32X-1.2X^{2}}{2+16X-0.4X^{2}}=-1.8$

The Production is inelastic