Using the following productions figures of a firm, derive the relationship between total product and marginal product.
Units of Land $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
Units of Labour $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$T P$ $0$ $4$ $11$ $25$ $37$ $41$ $43$ $43$ $41$

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Solution

Units of Land 1 1 1 1 1 1 1 1 1
Units of Labour 0 1 2 3 4 5 6 7 8
Total Product 0 4 11 25 37 41 43 43 41
Marginal Product 0 4 7 14 12 4 2 0 -2

Relation between Total Product $(M P)$ and Marginal Product $(M P)$ :
(i) Up to $3 r d$ unit of labour employment, $M P$ increases and $T P$ increases at increasing rate.
(ii) From $4 t h$ unit to $6 t h$ unit of labour employment, $M P$ decreases and $T P$ increases at diminishing rate.
(iii) At $7 t h$ unit of labour employment, $M P$ is zero and $T P$ is maximum.
(iv) At $8 t h$ unit of labour employment, $M P$ is negative and $T P$ starts declining.

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The following table gives the marginal product schedule of labour. It is given that total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour :

$\begin{matrix} L & 1 & 2 & 3 & 4 & 5 & 6 M P_{L} & 3 & 5 & 7 & 5 & 3 & 1 \end{matrix}$

Q. Simplify:
(i)

\frac{11}{12} \div (\frac{5}{9} \times \frac{18}{25})

(ii)

(2 \frac{1}{2} \times \frac{8}{10}) \div (1 \frac{1}{2} + \frac{5}{8})

(iii)

\frac{15}{16}

(\frac{5}{6} - \frac{1}{2}) \div \frac{10}{11}

(iv)

\frac{9}{8} \div \frac{3}{5}

(\frac{3}{4} + \frac{3}{5})

(v)

\frac{2}{5} \div {\frac{1}{5} o f [\frac{3}{4} - \frac{1}{2}] - 1}

(vi)

(1 \frac{3}{4} \times 3 \frac{1}{7}) - (4 \frac{3}{8} \div 5 \frac{3}{5})

Complete the following table

$\begin{matrix} U n i t o f L a b o u r & A v e r a g e P r o d u c t (u n i t s) & M a r g i n a l P r o d u c t (u n i t s) 1 & 8 & - 2 & 10 & - 3 & - & 10 4 & 9 & - 5 & - & 4 6 & 7 & - \end{matrix}$

The following table gives the marginal product schedule of labour. It is also given that total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour.

L	MP_L
1	3
2	5
3	7
4	5
5	3
6	1

Q. Simplify:

\frac{4 \frac{1}{7} - 2 \frac{1}{4}}{3 \frac{1}{2} + 1 \frac{1}{7}} \div \frac{1}{2 + \frac{1}{2 + \frac{1}{5 - \frac{1}{5}}}}

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Units of Land	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
Units of Labour	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$T P$	$0$	$4$	$11$	$25$	$37$	$41$	$43$	$43$	$41$

Using the following productions figures of a firm, derive the relationship between total product and marginal product.Units of Land111111111Units of Labour012345678TP0411253741434341

Using the following productions figures of a firm, derive the relationship between total product and marginal product.
Units of Land $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$
Units of Labour $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$T P$ $0$ $4$ $11$ $25$ $37$ $41$ $43$ $43$ $41$