Final answer:
The condition for cost-minimizing use of labor and capital in a production process is determined by the production isoquant, which represents the combinations of labor and capital that can produce a given level of output. The firm minimizes costs by choosing the combination with the lowest cost. At the cost-minimizing point, the ratios of the marginal product of labor to the wage rate and the marginal product of capital to the rental rate are equal.
Step-by-step explanation:
The condition for the cost-minimizing use of labor and capital in a production process is known as the production isoquant. It represents all the combinations of labor and capital that can produce a given level of output. The firm minimizes costs by choosing the combination of labor and capital that lies on the isoquant and has the lowest cost.
At the cost-minimizing point, the ratio of the marginal product of labor to the wage rate is equal to the ratio of the marginal product of capital to the rental rate. This ensures that the firm is allocating its resources efficiently and achieving the lowest cost of production.
For example, let's say a firm can produce 100 units of output using 10 units of labor and 5 units of capital, or it can produce the same 100 units of output using 5 units of labor and 10 units of capital. Both combinations have the same level of output, but the firm would choose the one with the lowest cost of labor and capital.