Chapter 7: Problem 18

How do we calculate each of the following: marginal cost, average total cost, and average variable cost?

Short Answer

Expert verified

To calculate marginal cost (MC), average total cost (ATC), and average variable cost (AVC) for a given quantity, use the following formulas: - Marginal Cost: $MC = \frac{\Delta TC}{\Delta Q}$, where ΔTC is the change in total cost, and ΔQ is the change in quantity. - Average Total Cost: $ATC = \frac{TC}{Q}$, where TC is the total cost, and Q is the quantity produced. - Average Variable Cost: $AVC = \frac{TVC}{Q}$, where TVC is the total variable cost, and Q is the quantity produced.

Step by step solution

Understand Marginal Cost

Marginal cost (MC) is the increase in the total cost that occurs when the quantity produced increases by one unit. It is calculated by finding the change in total cost divided by the change in quantity. The formula for marginal cost is: $MC = \frac{\Delta TC}{\Delta Q}$ where ΔTC is the change in total cost, and ΔQ is the change in quantity.

Understand Average Total Cost

Average total cost (ATC) is the total cost per unit of output. It is calculated by dividing the total cost (TC) by the quantity (Q) of output produced. The formula for average total cost is: $ATC = \frac{TC}{Q}$

Understand Average Variable Cost

Average variable cost (AVC) is the total variable cost per unit of output. Variable costs are those costs that vary with the level of production. It is calculated by dividing the total variable cost (TVC) by the quantity (Q) of output produced. The formula for average variable cost is: $AVC = \frac{TVC}{Q}$

Calculate Marginal Cost

To calculate the marginal cost, we need data on the total cost and the quantity produced. Suppose the total cost increases from $1000 to $1100 when the quantity produced increases from 50 to 51 units. We can calculate the marginal cost using the formula: $MC = \frac{\Delta TC}{\Delta Q} = \frac{1100 - 1000}{51 - 50} = \frac{100}{1} = 100$ The marginal cost of producing one more unit is $100.

Calculate Average Total Cost

To calculate the average total cost, we need data on the total cost and the quantity produced. Suppose the total cost is $1000 for producing 50 units. We can calculate the average total cost using the formula: $ATC = \frac{TC}{Q} = \frac{1000}{50} = 20$ The average total cost of production is $20 per unit.

Calculate Average Variable Cost

To calculate the average variable cost, we need data on the total variable cost and the quantity produced. Suppose the total variable cost is $800 for producing 50 units. We can calculate the average variable cost using the formula: $AVC = \frac{TVC}{Q} = \frac{800}{50} = 16$ The average variable cost of production is $16 per unit.

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