Question
Explain briefly the concept of equilibrium.

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Read the following case study carefully and answer the questions 1-2 on the basis of the same:
The production function is a mathematical expression which relates the quantity of factor inputs to the quantity of outputs that result. The short run production function is defined in economics as a period of time where at least one factor of production is assumed to be fixed. The analysis of short run production sets the stage to better understand the supply-side of the market. How producers respond to price depends, in part, on their ability to combine inputs to produce output. This ability is guided by the law of diminishing marginal returns, which states that the productivity of a variable input declines as more is added to a fixed input. If productivity declines, then more of the variable input is needed as the quantity produced increases. This results in an increase in production cost, which means producers need to receive a higher price.
- Bashir, Furrukh and others, Estimation of Short Run Production Function:
A Case Study of Shakarganj Mills Limited, 2011
1. Spell out the basic difference between the 'law of variable proportions', and 'returns to scale'.
2.  (i) Increasing returns to a factor are indicated whenever there it true? is increase in total product. Is
     (ii) Diminishing returns to a factor must lead to a fall in marginal product as well as total product. Is it true?
Calculate arithmetic mean from the following data:
x
f
Less than 10
5
Less than 20
15
Less than 30
55
Less than 40
75
Less than 50
100
Calculate arithmetic mean from the following data:
X
f
Less than 10
5
Less than 20
15
Less than 30
55
Less than 40
75
Less than 50
100
Distinguish between extension of demand and contraction of demand.
Scatter diagram studies correlation between two variables but it does not measure the precise extent of correlation. In the context of above statement explain the advantages and disadvantages of scatter diagram.
List some variables where accurate measurement is difficult.
How will you make choice of a suitable measure of dispersion?
Define Mode. Discuss its merits and demerits.