Short run costs for manufacture TC 100 +2Q +0.01Q2
To calculate the short run costs for manufacture, we need to understand the components of the Total Cost (TC) function you provided. The equation TC = 100 + 2Q + 0.01Q^2 represents a quadratic cost function, where Q is the quantity of output being produced.
Let's break down each component of the equation:
1. Fixed Costs (FC): The constant term in the equation, 100, represents the fixed costs. These are costs that do not change with the level of output and are incurred regardless of whether any units are produced.
2. Variable Costs (VC): The term 2Q represents the variable costs. These are costs that change as the level of output changes, typically due to factors like raw materials, direct labor, or energy consumption.
3. Quadratic Costs: The term 0.01Q^2 represents the quadratic costs. This component indicates that there might be economies or diseconomies of scale depending on the level of output. If Q^2 is positive, it suggests that the firm is experiencing diseconomies of scale, where increasing output leads to diminishing returns and higher costs per unit.
To calculate the short-run costs for a specific level of output (Q), substitute the value of Q into the total cost function and simplify the equation. For example, if you want to calculate the short-run cost for manufacturing 100 units (Q = 100), the calculation would be:
TC = 100 + 2(100) + 0.01(100)^2
= 100 + 200 + 1,000
= 1,300
Therefore, the short-run total cost for manufacturing 100 units would be 1,300 units of currency (whatever units you're using).
Note: The short run relates to a period in which at least some of the inputs used in production cannot be easily changed, such as plant size, while the long run allows all inputs to be adjusted.