Final answer:
To produce 2 units of output, a firm requires 3 units of factor 1 and 0.5 units of factor 2 with prices at $2 and $4 respectively. The minimum total cost of production using these inputs is $8. An isocost representing the lowest cost for producing 2 units of output with the given fixed proportions and input prices is a point where this total cost is incurred.
Step-by-step explanation:
The question relates to the determination of the lowest cost of production given a fixed technology condition, with fixed proportions between input factors. In this particular scenario, the firm's production function indicates that to produce 2 units of output, it requires 3 units of factor 1 and 0.5 units of factor 2. Cost minimization is achieved by adhering strictly to this combination when ordering inputs, as deviating from these proportions would not produce the desired output or would result in waste.
Given the prices for factor 1 and factor 2 being $2 per unit and $4 per unit respectively, we can calculate the minimum total cost for these factors needed to produce 2 units of output. The cost of factor 1 will be 3 units × $2/unit = $6, and the cost of factor 2 will be 0.5 units × $4/unit = $2. The minimum total cost of producing 2 units of output then is $6 + $2 = $8.
An isocost line represents all the combinations of inputs that give the same cost. For the minimum cost to produce 2 units of output using these factors, it will be a point where the total cost is $8. This point reflects the lowest cost combination of inputs given the prices of the factors and the fixed proportion technology.