• The law of variable proportions and returns to scale underlie the process of production.
• An important problem for an entrepreneur is deciding on the right combination of factors to produce a product.
• There are various technologies or techniques available to a firm for production, requiring the selection of the best combination of factors for a given output.
• Various combinations of factors yielding the same output are represented by an isoquant or equal product curve.
• An isoquant or iso-product map shows different technical possibilities for producing various levels of output.
• It is assumed that the entrepreneur aims to maximize profits.
• A profit-maximizing entrepreneur seeks to minimize costs for a given output or to maximize output for a given outlay.
• The choice of a particular combination of factors depends on:
  • Technical possibilities of production (represented by the isoquant map).
  • Prices of factors used in production.

• The choice of least-cost factor combination involves calculating the cost of different factor combinations available for production.
• Technologically feasible ways to produce a given output refer to different factor combinations that can produce a commodity.
• A profit-maximizing firm chooses a factor combination that minimizes cost for producing a given output.
• Factors can be substituted for each other to obtain the least-cost combination of factors.
• If labour wages rise, the firm will use labour-saving technology and substitute capital for labour (e.g., automate the assembly line).
• If capital becomes more expensive, the firm will substitute labour for capital, adopting more labour-intensive technology.
• A firm has to decide which production technique or technology to use from available alternatives to minimize the cost of producing a given output.
• Example: If a firm desires to produce 500 units of a commodity per week, it has 5 combinations of labour and capital(A, B, C, D, E) to choose from. All combinations can produce 500 units, but the firm will choose the one that minimizes cost.
• If the wage of labour is Rs 100 per day and the price of capital is Rs 50 per machine hour, the least-cost factor combination will be D (from the given table).
• If the wage of labour increases (to Rs 135 per day), and the price of capital remains the same, the firm will substitute capital for labour and switch to a more capital-using factor combination.
• Equi-marginal Productivity Rule: To minimize cost, the firm will equate the marginal product of the last rupee spent on each factor, similar to how a consumer maximizes satisfaction by equating marginal utility of the last rupee spent on each good.
• The Equi-marginal Productivity Rule:

$$\frac{M{P}_L}{P_L}=\frac{M{P}_K}{P_K}$$

Where:

• • MP_L is the marginal product of labour
  • MP_K is the marginal product of capital
  • P_L is the price of labour
  • P_K is the price of capital
• The firm chooses a factor combination such that the ratio of the marginal productivities of labour and capital is equal to their factor price ratio.
• Prices of factors are introduced into the study to determine the least-cost combination of factors.