Cost functions and cost curves, components and.pptx

Production

1. Cost functions and cost curves, components and cost minimization A.KARUNYALAKSHMI 2023504005

2. Cost function It refers to the relationship between input costs and output C = f (q) Where C – cost of production , q – quantity of production and f – functional relationship

3. COST FUNCTIONS Cost functions are derived functions. They are derived from the production function. Short run costs are costs over a period during which some factors of production are fixed. C = f ( X ,T , P f ,K ) Long run costs are costs over a period long enough to permit the change of all factors of production, all factors become variable. C = (X ,T , P f ) C = total costs , X= output , T= Technology , P f = prices of factors , K = fixed factors

4. Short-run costs Total cost is split into two groups : total fixed costs and total variable costs TC = TFC + TVC Fixed costs include salaries of administrative staff, depreciation of machinery , expenses for building depreciation and expenses for land maintenance Variable costs include the raw materials, cost of direct labour and running expenses of fixed capital

5. COMPONENTS : Total fixed costs : Total costs is denoted by straight line parallel to the output axis

6. Total variable costs Has an inverse S- shape which reflects law of variable proportions. According to this law, at the initial stages of production with a given plant , more of the variable factors is employed, its productivity increases and average variable cost falls.

7. Average fixed cost Average fixed cost is found by dividing TFC by the level of output AFC = TFC / X AFC is a rectangular hyperbola , showing at all its points the same magnitude , level of TFC

8. Average variable costs It is obtained by dividing TVC with the corresponding level of output : AVC = TVC/X

9. Average total costs ATC is obtained by dividing TC by the corresponding level of output ATC = TC / X = TFC + TVC/ X = AFC + AVC The shape of ATC is similar to AVC , U- shaped , reflecting law of variable proportions.

10. Marginal cost Marginal cost is the derivative of TC function , denoting total cost by C and output by X MC = MC is the slope of TC , it is U – shaped  

11. Long run costs The long run curve is a planning curve , it is a guide to the entrepreneur in his decision to plan the future expansion of his output. The long run average cost curve is derived from short run curves. Each point on LAC corresponds to a point on a short run cost curve , which is tangent to LAC at that point LAC is U- shaped and is often called the envelope curve as it envelopes the SRC curves U shape reflects the law of returns to scale.

12. Cost minimization In order to maximize profits, firms must minimize costs. Cost minimization simply implies that firms are maximizing their productivity or using the lowest cost amount of inputs to produce a specific output. In the short run, firms have fixed inputs, like capital, giving them less flexibility than in the long run. This lack of flexibility in the choice of inputs tends to result in higher costs Q = f(L ,K) where Q is output, L is the labor input, and K is capital.

13. Long run The long run, by definition, is a period of time when all inputs are variable.   Q=f(L,K) the total cost of production is the sum of the cost of the labor input,  𝐿 , and the capital input, K. The cost of labor is called the wage rate, w. The cost of capital is called the rental rate, r. The cost of the labor input is the wage rate multiplied by the amount of labor employed,  wL The cost of capital is the rental rate multiplied by the amount of capital,  rK The total cost ( C ), therefore, is C(Q)= wL + rK

14. Linear cost function TC = k + f( Q) TC – total cost . k is total fixed cost ,constant , f(Q) is variable cost When output is zero, total cost is equal to total fixed costs , if factor prices remain constant over a range of output, doubling of output leads to doubling of output – constant returns to variable factor In short run , capacity is fixed , so the firm can vary its rate of output up to capacity Average cost declines with expansion of output Marginal cost – d (TC)/ dQ , constant and linear cost function , horizontal line parallel to output axis.

15. Quadratic cost function I f there is diminishing return to the variable fac­tor the cost function becomes quadratic. There is a point beyond which TPP is not proportionate. Therefore, the marginal physical product of the vari­able factor will diminish. And if TPP actually falls MPP will be negative. In other words, there is a point beyond which additional increases in output cannot be made. So costs rise beyond this point, but output cannot .

16. Cubic cost function 1.When Q = 0, total cost is equal to total fixed cost. 2. Total fixed cost remains constant at levels of output up to capacity (as in the previous two cases). 3. With an output expansion there is an ini­tial stage of increasing return to the variable factor; thereafter a point is reached (the inflection point) at which there is constant return to the variable factor; finally, there is diminishing return to the variable factor.

17. Translog cost function The translog cost function expresses cost as a function of all input prices and quantity of output that is produced .for a given level of output y , the corresponding point on cost function is assumed to be minimum cost of producing y . The function is ln C* = + Σ lnv i + Σ Σ ij lnv i lnv j + ln y + Σ Σ iz lnv i lnz k ° + Σ yz lny lnz k ° + Σ Σ jk lnz k ° lnz k ° + Σ z lnz k ° + Σ lny lnv i where (v1,..., vn ) = the vector of input prices (z1,..., zn ) = the vector representing levels of the fixed inputs y = output = the parameter vector to be estimated It is used to model how the primary factors such as labour , capital is used to produce a single final output It is also being used in banking and financial sector to estimate marginal cost of production and elasticities of input demand  

18. Reference A . Koutsoyiannis , Modern microeconomics, Macmillan press, 1975 Ray, S. C. (1982). A translog cost function analysis of US agriculture, 1939–77.  American Journal of Agricultural Economics ,  64 (3), 490-498. Banda, H. S., & Verdugo, L. E. B. (2007). Translog cost functions: An application for Mexican manufacturing.  Banco de Mexico Documentos de Investigation Working papers .