Optimal Combination of factors of Production OR Equilibrium of the Firm

The point which maximize the profit of the firm or seller. The goal of the to maximize the difference between total revenue and total cost.

Assumptions
  1. The goal of the firm is to maximize the profit i.e. maximization of the difference between total revenue and total cost.
  2. The price of output is given P, the prices of factors are given: w is the given wage rate and r is the given price of capital.
Equilibrium Conditions For Firm

1st Condition: Slope of isoquant at equilibrium point is equal to the slope of isocost line i.e -dK/dL = w/r.
2nd Condition: At the point of equilibrium, the isoquant curve is convex to the origin.

When the above conditions are satisfied then the firm will be in equilibrium otherwise will not.

Two Possible Situations For a Firm Equilibrium

1st Situation: 1st situation is occur when the firm wants to maximize its profit with given cost constraint and with given price of output with the help of more output production.
If we see the diagram, the maximum output, the firm can produce with the given cost constraint and the optimal combination for maximum output is K1 and L1.

There are also higher level of output present and desirable but they are not attainable with the given cost constrain. Moreover at the equilibrium point E the slope of isoquant is equal to the slope of the isocost line.

2nd Condition: In 2nd condition, the firm will try to maximize its profit with a given level of output to decrease the cost on the output and maximize its profit.
From the diagram it is cleared that the firm is trying to maximize its profit with lower cost on the given level of output.

The combination of K1 and L1 shows the minimum cost for X output. There are also lower level of cost constraints present but with the help of them the given level of X output is not attainable and the point E shows the minimum cost combination of K1 and L1 for the given output X. At point E the isoquant curve is convex to the origin. It also shows the 2nd equilibrium condition for the firm.

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