Elasticity of supply may be defined as the degree of responsiveness of the quantity supplied of a commodity to change in its price.

Under geometric method, the elasticity of supply is measured at a point on the supply curve. To explain this method, let us draw three straight line supply curves.

To measure elasticity of supply at a point, we extend the supply curve so that its meets the x-axis at point B in its negative range, positive range and exactly at the point of origin. Elasticity of supply at a point (say A) is equal to the horizontal segment BC divided by the quantity supplied at point A. Thus,

\({ e }_{ s\quad }=\quad { BC }/{ OC }\)

In Fig.  (i), \({ e }_{ s }=\frac { BC }{ OC } >1\)                                              \(\left[ \because \quad BC\quad >\quad OC \right] \)

In Fig,  (ii), \({ e }_{ s }=\frac { BC }{ OC } <1\)                                                 \(\left[ \because \quad BC\quad <\quad OC \right] \)

In Fig,  (iii), \({ e }_{ s }=\frac { OC }{ OC } =1\)                                                  \(\left[ \because \quad BC\quad =\quad OC \right] \)

Thus, it can be concluded that:

a straight line supply curve which intersects the x-axis in its negative range implies e_s > 1

a straight line supply curve which intersects the x-axis in its positive range implies e_s < 1.

a straight line supply curve passing the origin implies e_s = 1irrespective of how steep or flat it is.

Under percentage method,  elasticity of supply is measured by dividing the percentage change in quantity supplied of a commodity by percentage change in its price.

                                          \({ e }_{ s }=\frac { Percentage\quad change\quad in\quad quantity\quad supplied }{ Percentage\quad change\quad in\quad price } \)

                                              \(=\frac { \triangle { q }/{ p\quad }\times \quad 100 }{ \triangle { p }/{ q\quad \times \quad 100\quad } } =\frac { \triangle { q }_{ s } }{ \triangle { p } } .\frac { p }{ { q }_{ s } } \)

 \(\therefore\)                                       \({ e }_{ s }=\frac { \triangle { q }_{ s } }{ \triangle { p } } .\frac { p }{ { q }_{ s } } \)

Example. 

p	q
10	100
20	200

                                           \({ e }_{ s }=\frac { \triangle { q }_{ s } }{ \triangle { p } } \times \frac { p }{ { q }_{ s } } =\frac { 100 }{ 10 } \times \frac { 10 }{ 100 } =1\)

Thus, \({ e }_{ s }\) is unity of 1.

(a) Relationship between TR and MR. MR represents addition to TR.

(i) When MR is positive, TR rises.

(ii) When MR = 0, TR is maximum.

(iii) When MR is negative, TR falls.

(iv) In case when MR becomes constant TR increases at a constant Rate

Qty sold (Q)	Price (P)	TR		MR
1 2 3	6 5 4	6 10 12	TR rises	6 4 2	MR > 0
4	3	12	TR max	0	MR = 0
5 6	2 1	10 6	TR falls	-2 -1	MR < 0

(b) Relationship between MR and AR

(i) When a firm is able to sell more quantity of output at the same price ti,e., under perfect competition) then AR and MR are equal and AR and MR curves take the shape of a straight line parallel to x-axis.

Q	P	TR	MR	AR/P
1	10	10	10	10
2	10	20	10	10
3	10	30	10	10
4	10	40	10	10

(ii) When a firm is able to sell more quantity of output only by lowering the price, then AR and MR both will be falling, i.e., sloping downward and MR will be less than AR. The rate of decline in MR is twice the rate of decline in AR.

Q	P	TR	MR	AR/P
1	4	4	4	4
2	3	6	2	3
3	2	6	0	2
4	1	4	-2	1

(i) Perfectly Inelastic Supply. It implies that quantity supplied of a commodity does not respond to change in its price.

                            \({e}_{s}=0\)

(ii) Less than Unit Elastic Supply. It implies that percentage change in quantity supplied of a commodity is less than percentage change in its price.

                                     \({e}_{s}<1\)

(iii) Unit Elastic Supply. It implies that percentage change in its quantity supplied is equal to percentage change in its price.

                             \({e}_{s}=1\)

(iv) More than Unit Supply. It implies that percentage change in its quantity supplied is more than percentage change in its price.

                 \({e}_{s}>1\)

(v) Perfectly Elastic Supply. It implies that its quantity supplied changes irrespective of no change in its prIce

                \({ e }_{ s }=\infty \)

The producer's equilibrium condition's are (i) MC = MR and (ii) MC > MR after equilibrium, i.e., MC = MR.

  (i) When MC > MR: In this situation, it will be profitable for the given firm to produce more or less depending upon relative changes in MC and MR till MC = MR.

  (ii) When MC < MR: It will be profitable for the producer to produce more till MC = MR.

MC = MR is not a sufficient condition to ensure equilibrium. Given MC = MR, suppose the behaviour of MC and MR is such that if one more unit is produced MC becomes less than MR. Then, in this case, it would be profitable for the firm to produce more. Therefore, in this case, though MC = MR, the producer is not in equilibrium.

However, if after MC = MR output, MC becomes greater than MR, it will be most advantageous for the firm to produce only upto MC = MR.

Explicit Cost	Implicit Cost
(a) Explicit cost are the costs which are incurred by making payments to the factors hired or purchased.	Implicit cost are the costs which are estimated value of inputs provided by the owners themselves.
(b) It is 'paid-out' cost.	It is 'paid-in' cost
(c) Examples: Payment of wages, payment of rent, purchases of raw materials.	Examples: rent of the owner-occupied building, salary for own labour supplied

(i) 

Fixed Costs	Variables Costs
(a) Fixed Cost are the Costs which do not change with change in the level of output.	Variable costs are the costs which directly change with change in the level of output.
(b) These costs remam even if the output is zero	There are no variable costs at zero level of output.
(c) Example: Rent for factory building, wages to permanent staff, interest in on capital ete.	Example: Expenses on raw material used in production, wages to daily workers ete.

(ii)

Average Cost	Marginal Cost
(a) Average cost is per unit cost of production.	Marginal cost IS addition made to total cost when an additional unit of commodity is produced.
(b) It is calculated by dividing the total cost by number of units produced AC = Total Cost/No. of units produced.                           \(AC=\frac{TC}{Q}\)	Marginal cost IS addition made to total cost when an additional unit of commodity is produced
(c) AC=AFC+AVC	It is calculated by dividing the change in total variable cost by change in number of units produced.                         \(MC=\frac { \triangle TVC }{ \triangle Q } \) \(M{ C }_{ n }=TV{ C }_{ n }-TV{ C }_{ n-1 }\)

The three phases of changes in Total Product and Marginal Product in the Law of Variable proportions are:

(i) Phase I: Total product rises at an increasing rate, i.e., upto point 'N.in the given diagram whereas Marginal Y product rises upto point 'a'.

(ii) Phase II: Total product rises at a decreasing rate, i.e., between point 'N. and point 'B' in the diagram. Marginal product falls and remains positive between point 'a' and 'b'.

(iii) Phase III: Total product falls after point 'B' and MP falls and becomes negative, i.e., after point 'b'.

Returns to a factor. When a variable factor increase, given the quantity of fixed factor, the resultant increase in output is called returns to a factor.

There are three phases of the law of variable proportions:

Phase I' (Increasing Returns to a Factor).  In the first phase, we have increasing returns to a factor. The total product (TP) increases at an increasing rate and the Marginal product (MP) is increasing. his phase ends at the point where MP reaches its highest point.

Phase II (Diminishing Returns to a Factor). In the second phase, we have
diminishing returns to a factor. The total physical product (TP) increases at a diminishing rate till it reaches the maximum point. Marginal' product (MP) is falling but is positive. This phase is crucial because the firms would like to produce in this stage.

Phase III (Negative Returns to a Factor). This is the phase of negative returns. Here the total product (TP) starts falling and Marginal product becomes negative and goes below x-axis.

The law of variable proportions states that if we go on using more and more units of a variable factor (labour) with a fixed factor (land), the total product increases at an increasing rate in the beginning.Then increases at a diminishing .rate and after a level of output .it ultimately falls. In accordance with law, the marginal physical product increases in the beginning, then it starts falling but remains positive and ultimately it continues to fall and also becomes negative.

The given diagram illustrates the law.The diagram shows that there are three phases of the law of variable proportions. In phase I, TP increases at an increasing rate and MP rises. In phase II, TP increases at decreasing rate and MP falls but remains positive. In phase III, TP starts falling and MP becomes negative. Phase I
is upto point M and phase II is from point M to point T. Phase III is after T.

Phase I. (Increasing returns to a factor) In this phase Total Product increases at increasing rate.

Reasons. In phase I, we get increasing returns to a variable factor because greater use of the variable factor makes it possible to utilize the fixed factor more fully and also to introduce a greater division of labour. Phase II. (Diminishing returns to a factor). In this phase total physical product increases at diminishing rate. This phase ends at the point when TPP reaches its highest point.

Reasons. In phase II, we get diminishing returns to the variable factor because in this stage the proportion between the variable factor and the fixed factor has crossed the optimum proportion between them. Phase H l , (Negative returns to a factor). In this phase, Total Physical Product starts sloping downward.

Reasons. In phase III, the variable factor becomes too much, which yields negative marginal product.

The law of variable proportions states that if we go on using more and more units of a variable factor (labour) with a fixed factor (land), the total product increases at an increasing rate in the beginning.Then increases at a diminishing .rate and after a level of output .it ultimately falls. In accordance with law, the marginal physical product increases in the beginning, then it starts falling but remains positive and ultimately it continues to fall and also becomes negative.

The given diagram illustrates the law.The diagram shows that there are three phases of the law of variable proportions. In phase I, TP increases at an increasing rate and MP rises. In phase II, TP increases at decreasing rate and MP falls but remains positive. In phase III, TP starts falling and MP becomes negative. Phase I
is upto point M and phase II is from point M to point T. Phase III is after T.

Phase I. (Increasing returns to a factor) In this phase Total Product increases at increasing rate.

Reasons. In phase I, we get increasing returns to a variable factor because greater use of the variable factor makes it possible to utilize the fixed factor more fully and also to introduce a greater division of labour. Phase II. (Diminishing returns to a factor). In this phase total physical product increases at diminishing rate. This phase ends at the point when TPP reaches its highest point. Reasons. In phase II, we get diminishing returns to the variable factor because in this stage the proportion between the variable factor and the fixed factor has crossed the optimum proportion between them. Phase H l , (Negative returns to a factor). In this phase, Total Physical Product starts sloping downward. Reasons. In phase III, the variable factor becomes too much, which yields negative marginal product.