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How to Understand and Calculate Cost Measures

Using Cost Data From a Linear Equation

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In this section we will look at how you calculate marginal cost, total cost, fixed cost, total variable cost, average total cost, average fixed cost, and average variable cost when you have a linear relationship between total cost and quantity. These are equations such as TC = 400Q + 20, or TC = 50 + 6Q. Equations such as TC = 34Q3 – 24Q + 9 or TC = Q – log(Q+1). are non-linear and will be looked at in the next section. We will examine all seven of our cost definitions using the equation TC = 50 + 6Q.

Marginal Cost

Marginal cost is the additional cost we have when we produce one more unit of the good. With the equation TC = 50 + 6Q, our total cost goes up by 6 whenever we add an additional good, as shown by the coefficient in front of the Q. So we have a constant marginal cost of 6 per unit produced.

Total Cost

We already have a formulation for the total cost, which is TC = 50 + 6Q. If we want to calculate the total cost for a specific quantity, all we need to do is substitute the quantity in for Q. So the total cost of producing 10 units is 50 + 6*10 = 110.

Fixed Cost

Our fixed cost is the costs we incur when we do not produce any units. So we substitute in Q = 0 to our equation and we get 50 + 6*0 = 50. So our fixed cost is 50.

Total Variable Costs

These are the non-fixed costs we incur when we produce Q units. So our variable costs are:

Total Variable Costs = Total Costs – Fixed Costs.

In our case that would be 50 +6Q – 50 = 6Q. So our total variable costs are 6Q, and we can calculate our total variable costs at a given point by substituting for Q.

Average Total Costs

We are averaging our total costs over the number of units we produce. So we take our total cost formula of TC = 50 + 6Q, and divide the right hand side to get average total costs. So our average total costs are AC = 50/Q + Q/Q = 50/Q + 6. To get our average total cost at a specific point we just substitute for the Q. So our average total cost of producing 5 units is 50/5 + 6 = 10 + 6 = 16.

Average Fixed Costs

Similarly, we just divide our fixed costs by the number of units we produce. Since our fixed costs are 50, our average fixed costs are 50/Q.

Average Variable Costs

As you may have guessed, to calculate our average variable costs we divide our variable costs by Q. Since our variable costs are 6Q, our average variable costs are 6. Notice that our average variable cost does not depend on our quantity produced and is the same as our marginal cost. This is one of the special features of the linear model, but will not hold when we use a non-linear formulation.

Be sure to continue to section 3 where we look at calculating all seven cost measures when given a linear equation.

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