A profit maximisation firm faces two choices of optimal combination of factors inputs. Thus the least cost combination of factors refers to a firm producing the largest volume of output from a given cost and producing a given level of output with the minimum cost when the factors are combined in an optimum manner.
We study these cases separately.
In the theory of production, the profit maximisation firm is in equilibrium when, given the cost-price function, it maximises its profits on the basis of the least cost combination of factors. For this, it will choose that combination which minimizes its cost of production for a given output.
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This will be the optimal combination for it. Given these assumptions, the point of least-cost combination of factors for a given level of output is where the isoquant curve is tangent to an iso-cost line. In Figure 17, the iso-cost line GH is tangent to the isoquant at point M.
At this point, the firm is minimising its cost for producing units. Any other combination on the isoquant , such as R or T, is on the higher iso-cost line KP which shows higher cost of production.
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The iso-cost line EF shows lower cost but output cannot be attained with it. Therefore, the firm will choose the minimum cost point M which is the least-cost factor combination for producing units of output.
Producer's Equilibrium (Hindi)
M is thus the optimal combination for the firm. There are two essential or second order conditions for the equilibrium of the firm:.
The first condition is that the slope of the iso-cost line must equal the slope of the isoquant curve. The slope of the iso-cost line is equal to the ratio of the price of labour w to the price of capital r i. The second condition is that at the point of tangency, the isoquant curve must he convex to the origin.
In other words, the marginal rate of technical substitution of labour for capital MRTS LC must be diminishing at the point of tangency for equilibrium to be stable.
In Figure 18, S cannot be the point of equilibrium, for the isoquant IQ 1 is concave where it is tangent to the iso-cost line GH. At point S, the marginal rate of technical.
If it decides to produce at EF cost, it can produce the entire output with only OF labour. Both the situations are impossibilities because nothing can be produced either with only labour or only capital.
Therefore, the firm can produce the same level of output at point M where the isoquant curve IQ is convex to the origin and is tangent to the iso-cost line GH. The firm also maximises its profits by maximising its output, given its cost outlay and the prices of the two factors.
This analysis is based on the same assumptions, as given above. The firm is in equilibrium at point P where the isoquant curve is tangent to the iso-cost line CL in Figure At this point, the firm is maximising its output level of units by employing the optimal combination of OM of capital and ON of labour, given its cost outlay CL. But it cannot be at points E or F on the iso-cost line CL, since both points give a smaller quantity of output, being on the isoquant , than on the isoquant The firm can reach the optimal factor combination level of maximum output by moving along the iso-cost line CL from either point E or F to point P.
This movement involves no extra cost because the firm remains on the same iso-cost line. The firm cannot attain a higher level of output such as isoquant because of the cost constraint.
At point P, the slope of the isoquant curve is equal to the slope of the iso-cost line CL. The second condition is that the isoquant curve must be convex to the origin at the point of tangency with the iso-cost line, as explained above in terms of Figure