Question

Consider the production function: Y= (a) Derive marginal physical product and average physical product equations. (b) Calculate the value of X when MPP is equal to zero. (c) Calculate the value of X when MPP cut APP at its maximum point and the transition that is happening in terms of Phases of production? (d) Justify why stage/phase two of production is regarded as rational stage. 

Answer 1

(a)

$MPP =\frac{ (TPP_2 - TPP_1)}{(X_2 - X_1)}$

$APP = \frac{TPP}{X}$

(b)

when MPP =0,

$0 =\frac{ (TPP_2 - TPP_1)}{(X_2 - X_1)}$

Therefore, $X =\infin$

When MPP=0, the value of X is maximum

(c)

$MPP=APP\\$

$\frac{ (TPP_2 - TPP_1)}{(X_2 - X_1)}= \frac{TPP}{X}$

$X(TPP_2-TPP_1)=TPP(X_2-X_1)$

$X=\frac{TPP(X_2-X_1)}{TPP_2-TPP_1}$

(d)

Stage ii is regarded as the rational stage of production because

Despite the decline in APP when more variable input is used MPP is still positive; that is, TPP still increases as a result of using more variable input. This stage holds until the point MPP=0