in the given case, payment of salary to the manager is the explicit cost because it is a payment to outsider.The use of own saving in starting the business constitutes implicit cost because it is the cost of self-employed resource.

In the given case, the labour cost of the family members constitutes implicit cost because it is the cost of self-employed resources.The rent paid on a firm is the explicit cost because it is the cost of outside resources.

The Law of variable Proportions explains the behaviour of Total Product ~nd Marginal Product. It states that when more and more units of a variable factor are employed, keeping the other factors fixed, the Total Product (TP) first increases at an increasing rate, then increases at a diminishing rate and finally starts falling.The different phases in the behaviour of TP and MP can be explained as below.

The production function is given as:   \(Q=5L+2K\) 
Substituting L=0 and K=10 in (I)we get:      ..............(1)
Q = 5(0) + 2(10)
= 0 + 20
= 20
Thus, the maximum possible output that the firm can produce with 0 units of L and 10 units of K is 20 units.

Total product is defined as the sum total of output produced by a firm by employing a particular input. It is also known as the Total Physical Product and is represented as
\(\mathrm{TP}=\sum Q_{x}\)
Where, ∑ represents summation of all outputs and Q_x represents units of output x produced by an input.

Short run:-
In short run, a firm cannot change all the inputs, which means that the output can be increased (decreased) only by employing more (less) of the variable factor (labour). It is generally assumed that in short run a firm does not have sufficient or enough time to vary its fixed factors such as, installing a new machine, etc. Hence, the output levels vary only because of varying employment levels of the variable factor.
Algebraically, the short run production function is expressed as
\(Q_{x}=f(L, \bar{K})\)
Where,
Q_x = units of output x produced
L = labour input
\(\bar{K}\)= constant units of capital
Long run:-
In long run, a firm can change all its inputs, which means that the output can be increased (decreased) by employing more (less) of both the inputs − variable and fixed factors. In the long run, all inputs (including capital) are variable and can be changed according to the required levels of output. The law that explains this long run concept is called returns to scale. The long run production function is expressed as
Q_x = f (L, K)
Both L and K are variable and can be varied.

(i) Following are the points of difference between Fixed Cost and Variable Cost:

(ii) Following  are the points of difference between Average Cost and Marginal Cost

The relationship between Total Cost (TC) and Marginal Cost (MC) is given below:
(i) Marginal Cost is estimated as the difference between the Total Cost of two successive units of capital. That is
\(MC_{ q }=TC_{ q }-TC_{ q-1 }\\ orMC=\frac { \Delta TC }{ \Delta q } \)
(ii) When MC is diminishing,TC increases at a diminishing rate.
(iii)When MC is rising,TC increases at an increasing rate.
(iv) When MC reaches its lowest point, TC stops increasing at a decreasing rate

The factors of production can be classified as fixed and variable factors. The fixed factors cannot be changed over a short period. The Law of Variable Proportions (or the Law of Returns to a Factor) states that when more and more units of a variable factor are employed, keeping the other factors  fixed, the Total Product (TP) first increases at an increasing rate, then increases at a diminishing rate and finallIy starts falling.The law explains the change in output due to the change in the proportions between the fixed and variable factors. The law of returns to a factor can be explained with the help of following diagram:

Stage I: Increasing Returns to Variable Factor
The Total Product (TP) increases at an increasing rate from 0 to \(L_{ 1 }\)  units of labour. That is, Marginal Product (MP) is increasing.
Stage 2: Diminishing Returns to Variable Factor
The Total Product (TP) increases at a diminishing rate from \(L_{ 1 }\) , to \(L_{ 2 }\)  units of labour. That is, Marginal Product (MP) is decreasing. MP is 0 at \(L_{ 2 }\) units of labour. •
Stage 3: Negative Returns to Variable Factor
The Total Product (TP) is decreasing beyond ~ units of labour. The output decreases as an additional unit of labour is employed. That is, Marginal Product (MP) is negative.

Increasing returns to scale implies that a proportionate change in the output is greater than the proportionate change in input. For example, the output increases by 20 percent due to 15 percent increase in all the inputs. Increasing returns to scale are due to economies of scale. Economies of scale indica e that long run Average Cost decreases, which corresponds to increasing returns to scale in terms 0 output. Economies of scale can be classified as::
1. Internal Economies of Scale: These include
(i) Technical Economies
(ii) Financial Economies
(iii) Marketing Economies
(iv) Managerial Economies
(v) Labour Economies
(vi) Risk-bearing Economies
(vii) Economies due to Indivisibilities
2. External Economies of Scale:These include
(i) Economies of Concentration
(ii) Economies of Information
(iii) Economies of Disintegration

Total Fixed Cost (TFC)
This refers to the costs incurred by a firm in order to acquire the fixed factors for production like cost of machinery, buildings, depreciation, etc. In short run, fixed factors cannot vary and accordingly the fixed cost remains the same through all output levels. These are also called overhead costs.
Total Variable Cost (TVC)
This refers to the costs incurred by a firm on variable inputs for production. As we increase quantities of variable inputs, accordingly the variable cost also goes up. It is also called ‘Prime cost’ or ‘Direct cost’ and includes expenses like − wages of labour, fuel expenses, etc.
Total Cost (TC)
The sum of total fixed cost and total variable cost is called the total cost.
Total cost = Total fixed cost + Total variable cost
TC = TFC + TVC

Relationship between TC, TFC, and TVC
1) TFC curve remains constant throughout all the levels of output as fixed factor is constant in short run.
2) TVC rises as the output is increased by employing more and more of labour units. Till point Z, TVC rises at a decreasing rate, and so the TC curve also follows the same pattern.
3) The difference between TC and TVC is equivalent to TFC.
4) After point Z, TVC rises at an increasing rate and therefore TC also rises at an increasing rate.
5) Both TVC and TFC is derived from TC i.e. TC = TVC + TFC