Production Function Calculation
The problem asks us to calculate the output level ($Q$) using a given production function and specific amounts of capital ($K$) and labour ($L$).
The production function is given by:
$ Q = 2 \cdot K^{1/3} \cdot L^{2/3} $
We are provided with the following input values:
- Capital ($K$): 8 units
- Labour ($L$): 27 units
Calculating Output Level
Substitute the given values of $K$ and $L$ into the production function:
$ Q = 2 \cdot (8)^{1/3} \cdot (27)^{2/3} $
Now, let's calculate the terms involving exponents:
- The cube root of 8, which is $8^{1/3}$, equals 2.
- To calculate $(27)^{2/3}$, we first find the cube root of 27 ($27^{1/3}$), which is 3. Then, we square this result: $3^2 = 9$.
Substitute these calculated values back into the equation for $Q$:
$ Q = 2 \cdot 2 \cdot 9 $
Performing the final multiplication:
$ Q = 4 \cdot 9 $
$ Q = 36 $
Therefore, the output level is 36 units when 8 units of capital and 27 units of labour are used.
Important Questions from Production Function
- Match the stages of production with their corresponding characteristics :
(i) Stage-I (a) Total product declines, Marginal product is negative (ii) Stage-II (b) Total product increases at an increasing rate, marginal product positive (iii) Stage-III (c) Total product increases at a diminishing rate, marginal product is zero. - Neo-classical production function has which of the following characteristics ?
(a) Positive and diminishing marginal productivities of the factors
(b) Constant returns to scale
(c) Satisfies Inada conditions
Choose the correct answer from the code below : - Which one of the following is not an Hirofumi Ujawa condition for a well behaved production function ?
- Exponents of the Cobb-Douglas production represent :
- When the quantity food production is done continuously every day, with no peaks and troughs of activity in production centres, it is termed as :
