PAC - Cost Functions Lesson
Cost Functions Lesson
Productivity and costs are closely related. Remember that in perfect competition, firms are price takers. As a result, firms have no real control over revenue, but they can control their costs. Therefore, the firm will place special importance on the productivity of inputs because productivity will directly impact whether costs are increasing or decreasing at the firm. There are seven basic cost functions for any firm: Total Fixed Cost, Total Variable Cost, Total Cost, Average Total Cost, Average Variable Cost, Average Fixed Cost, and Marginal Cost.
Total Fixed Cost
Total fixed cost is generally defined as the cost of capital and other short run fixed inputs. This is a cost that does not change with production. That is, no matter if the firm produces 0 units of output or 1,000 units of output, total fixed cost remains the same. An example of short run fixed cost is rent. For example, if you run a pizza restaurant, the $1,200 per month rent is a fixed cost. It is fixed for a variety of reasons. First, the term of the lease fixes the rent for the given time period. Furthermore, the rent does not increase or decrease based on the number of pizzas the restaurant produces.
Total Variable Cost
Total Variable Cost (TVC) reveals how much money the firm is spending for all its variable inputs/resources. For the purpose of this unit, labor is the only variable input. Therefore, TVC is wage multiplied by the number of laborers. TVC = W x L. If in the case of the pizza restaurant, you employ 6 workers at a wage of $500 each per month, your TVC equals $3,000. If you want to produce more pizzas, additional workers would need to be hired and TVC would increase. If you want to produce fewer pizzas, workers could be laid off and TVC would decrease.
Total Cost
Total Cost is the sum of Total Variable Cost and Total Fixed Cost. TC = TVC + TFC (please note: this equation can be rearranged to solve for TVC and TFC). Given the fixed and variable cost information above, the TC for the pizza restaurant (per month) would be $4,200.
Average Fixed Cost
Average Fixed Cost (AFC) is the firm's measure of how much money it is spending on fixed resources per unit. AFC = TFC/Q. It is important to note that AFC will always decrease as output is expanded. This is because the numerator (TFC) is constant and the denominator (quantity) is increasing. If the pizza restaurant produces 300 pizzas per month, the AFC is $4. That means, on average, each pizza accounts for $4 worth of fixed cost at the firm.
Average Variable Cost
Average Variable Cost (AVC) is the firm's measure of how much money it is spending on variable resources per unit. Specifically, for our analysis, AVC is the per unit labor cost for the firm. AVC = TVC/Q or AVC = ATC - AFC. If the pizza restaurant produces 300 pizzas per month, the AVC is $10.00. That means, on average, each pizza accounts for $10 worth of variable cost.
Average Total Cost
Average Total Cost (ATC) represents an even distribution of total costs across all units of output produced by the firm. It is the per unit cost of production. ATC = TC/Q. Furthermore, since TC = TVC + TFC, then ATC = AVC + AFC (please note: this equation can be rearranged to solve for AVC and AFC). In our pizza scenario, ATC can be found by dividing $4,200 by 300 pizzas. This would yield an ATC of $14 per pizza. It can also be found by adding AVC and AFC, $10 + $4 = $14.
Marginal Cost
This cost concept will be central in determining the profit maximizing level of output for a firm when considered along with marginal revenue in a later module. MC can be found by dividing the change in TC by the change in quantity, MC = ΔTC/ΔQ. Also, since the only reason TC changes is because TVC changes, it can be viewed as MC = ΔTVC/ΔQ. Suppose the pizza restaurant decides to increase its pizza production from 300 pizzas per month to 400 pizzas per month. The total cost at the firm goes from $4,200 per month to $4,700 per month (the firm had to hire an additional worker to increase pizza production). MC = ΔTC/ΔQ = $500/100 = $5.00. So, each of the additional 100 pizzas increases the costs at the firm by $5.00.
Marginal Cost is the basis for a firm's individual supply curve. Due to diminishing returns to labor, MC rises over the majority of the range of production. Since the additional cost (MC) of production for each unit is increasing, the firm will only be willing to supply those units if the price rises. This is the basis for the Law of Supply.
Fixed and Variable Costs Video
Please view the video below for more information and examples relating to these basic cost measures. To make the video full screen, click the double arrows at the bottom right corner of the object.
Types of Costs Review Activity
Use the following activity to help you review the different types of costs.
How are the Productivity and Cost Measures Related?
In the descriptions above, we took a cursory look at the relationship between costs and quantity produced. In order to fully understand the upcoming graphs for costs, it is necessary to dig a little deeper into the significance of productivity. A solid understanding of marginal product, average product, and their relationship is necessary for understanding the behavior of the cost functions.
Productivity and Costs in the Short Run Video
The video below walks you through these relationships and their impact on costs. You will want to take notes on this video. To make the video full screen, click the double arrows at the bottom right corner of the object.
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