(a) CASE - A

\(PES=\frac { \triangle Q }{ \triangle P } \times \frac { P }{ Q } =\frac { 20 }{ 1 } \times \frac { 2 }{ 40 } =1\)
 CASE -B

\(PES=\frac { \triangle Q }{ \triangle P } \times \frac { P }{ Q } =\frac { 20 }{ 1 } \times \frac { 2 }{ 20 } =2\)
(b) The supply elasticity differs in two cases even though absolute change in quantity supplied is 20 units in both the cases because, In case A, initial quantity = 40 and in case B initial quantity = 20 or we can say that in case A, percentage change in quantity supplied is equal to percentage change in price and in case B, percentage change in quantity supplied is greater than percentage change in price.

We have,

Percentage change in price = \(\frac { \triangle P }{ P } \times 100=\frac { 1 }{ 5 } \times 100\)=20%
PES=\(\frac { Percentage\ change\ in\ quantity\ supplied }{ Percentage\ change\ in\ price } =\frac { 20\%}{ 20 \%} =1\)
PES = 1 [Unitary Elastic supply]

Percentage change in price =\(\frac { \triangle P }{ P } \times 100=\frac { 2 }{ 10 } \times 100=20\%\)
Percentage change in supply = \({{\triangle Q}\over{Q}}\times 100={25\over 125}\times100=20\%\)
ES = 1 (Supply is unit elastic)
ES is always positive due to direct relationship between price and quantity supplied.

\(ES=\frac { percentage\ change\ in\ quantity\ supplied }{ Percentage\ change\ in\ price } ={{100\%}\over{50\%}}=2\)
ES = 2 (Supply is highly elastic as ES > 1)
ES is always positive due to direct relationship between price and quantity supplied.

Price Elasticity of Supply (ES) =
\(\frac { \triangle Q }{ \triangle P } \times \frac { P }{ Q } =\frac { 150 }{ 3 } \times \frac { 12 }{ 500 } =1.2\)
ES = 1.2 (Supply is highly elastic as ES > 1)
ES is always positive due to direct relationship between price and quantity supplied.

Price Elasticity of Supply (ES)=\(\frac { \triangle Q }{ \triangle P } \times \frac { P }{ Q } =\frac { 200 }{ 5 } \times \frac { 50 }{ 1000 } =2\)
ES = 2 (Supply is highly elastic as ES > 1)
ES is always positive due to direct relationship between price and quantity supplied.

Case1- Rise in Price of other Goods: As we mow price of other goods are inversely related to the supply of given commodity. So, when there is rise in price of other product, the supply curve of given commodity decreases and shifting the supply curve to the left as shown in the given figure.

Case ll- Fall in price of Other goods: As, against it, if there is fall in price of other product, the supply curve of a given commodity increase and shifting the supply curve to the right as shown below:

Case 1- When price of input rises: Due to rise in price of input the cost of production of a firm increases, which will thereby decrease the supply curve to the left as shown in the given figure.

Case ll- When price of input falls: Due to fall in price of input, the cost of production of a firm decreases which will thereby increase the supply curve to the right as shown in the given figure.

A decrease in supply means that producers now supply less at a given price level. The conditions are:
(a) Rise in the prices of remuneration of factors of production.
(b) Rise in the prices of other goods.
(c) When the technology becomes outdated.
(d) Change in the objective of producer (decrease supply at the same price).
(e) Taxation policy of government rises.

(i) In the short period, supply is relatively less elastic as firm can change the supply by changing the variable factors only, as fixed factors remain fixed during short period.
(ii) The supply curve during short period is inelastic, i.e., percentage change in quantity supplied is less than percentage change in price as shown below:

(i) The degree of responsiveness of quantity supplied to the changes in price of the commodity is known as price elasticity of supply.
(ii) Percentage Method: To measure price elasticity of supply, we use percentage method. According to this method, elasticity is measured as the ratio of percentage change in the quantity supplied to percentage change in the price. Price elasticity of supply (ES)
\(=\frac { Percentage\ change\ in\ quantity\ supplied }{ Percentage\ change\ in\ price } \)
Where,
Percentage change in quantity supplied
\(=\frac { change\ in\ quantity\ supplied(\triangle Q) }{ Initial\ Quantity\ Supplied(Q) } \)X100
Change in Quantity \((\triangle Q)\)
=New Quantity(Q₁)-Initial Quantity(Q) 
Percentage change in price
\(=\frac { change\ in\ Price(\triangle P) }{ Initial\ Price(P) } \times 100\)
Change in price \((\triangle P)\)=New price (P₁)-Initial Price (P)
Proportionate Method:
The percentage method can also be converted into the proportionate method. Putting the values of 1, 2, 3 and 4 in the formula of percentage method, we get, 
\(ES=\frac { \frac { \triangle Q }{ Q } \times 100 }{ \frac { \triangle P }{ P } \times 100 } =\frac { \frac { \triangle Q }{ Q } }{ \frac { \triangle P }{ P } } \)
Elasticity of Supply (Proportionate Method)=\(\frac { \triangle Q }{ \triangle P } \times \frac { P }{ Q } \)
Where, Q = Initial Quantity Supplied
\(\triangle \)Q = Change in Quantity Supplied
P = Initial Price
\(\triangle \)P = Change in Price

(i) When the number of firms in the industry increases, market supply also increases due to large number of producers producing that commodity.
(ii) So, due to increase in market supply, the supply curve shifts rightward as shown.

(i) This also influences the supply since price of inputs (rent, wages, interest, profit) constitutes the cost of production of a commodity.
(ii) An increase in the price of an input may lead to rise in cost of production, which will thereby decrease the production of a commodity shifting the supply curve to the left as shown.

Note: As the three firms are identical, supply of the second firm (SS₂) and the third firm (SS₃) will be equal to the supply of first firm (SS₁).