Khan Academy
Unit 3: Production, Cost, Perfect Competition Model
In economics, a "perfect" market is a theoretical market in which there are many buyers and sellers, and where no one has an advantage over others. In this unit, you'll learn how perfect markets can be used to model relationships between productivity and costs and competition between firms.
Lesson 1: The Production Function
Introduction to Production Functions
Production functions describe how output is determined by various inputs. The short run is defined as the period of time in which at least one input is fixed. Anything longer than that is considered the long run.
Production Function: Various inputs put into a process, and the function would describe how much output given that input
Output, used in Q in economics, is gonna be a function of the various inputs: Q = f(I#1, I#2, …)
Inputs would be classic factors of production (land, labor, capital, entrepreneurship)
Example: Bread toasting operation
Inputs: Bread, toaster (4 slices in 10 minutes), labor to operate toaster (1 slice per minute)
Output: # of slices of toasted bread per hour = min(slices of bread per hour, 24 slices per hour x toasters, 60 x workers)
Short run: At least one input is fixed
Long run: Longer than the short run
Total Product, Marginal Product, and Average Product
The short-run production function describes the relationship between output and inputs when at least one input is fixed, such as out output varies based on the amount of labor used. We can use this production function to find the total product of labor, the marginal product of labor, and the average product of labor.
How does output vary based on one input?
Example: Running ice-cream factory, as varied by how many workers
Labor (Workers per Day) | Total Production (Gallons per Day) | Marginal Production | Average Product |
0 | 0 | ||
1 | 10 | 10 | 10/1 = 10g |
2 | 18 | 8 | 18/2 = 9g |
3 | 24 | 6 | 24/3 = 8g |
Diminishing Marginal Return: Marginal production decreases as inputs increase
Causes concave down curve of total product v labor graph
Increasing the quantity of capital avoids diminishing marginal returns
Marginal Product: Change of output / Change of input
If total product is maximized, marginal product = 0, because adding another unit of input creates no additional output
Average Product: Total product / labor (or varying input)
Acquiring more of another resource will shift the labor curve upwards, because it can produce more at every quantity of labor
Lesson 2: Short-run Production Costs
Fixed, Variable, and Marginal Cost
Explore how to think about average fixed, variable, and marginal costs, and how to calculate them, using a firm's production function and costs in this video.
Example: Finding the optimal numbers of programmers to hire
Consider fixed costs (office base, electricity, product manager salary, etc.), variable costs (full compensation of salaries, health insurance compensation, etc.)
Fixed costs: Won’t change per unit of production
Variable costs: Linearly increasing per unit of production
Total costs: Fixed + Variable costs
Average fixed costs: Fixed costs / output
Marginal will decrease, individual productivity decrease
Average variable costs: Variable costs / output
Marginal will increase
Average total costs: Total costs / output
Marginal will decrease at first then increase
Marginal costs: Change in total costs / change in outputs
Increase then becomes negative
Marginal Cost, Average Variable Cost, and Average Total Cost
In this video we calculate the costs of producing a good, including fixed costs, variable costs, marginal cost, average variable cost, average fixed cost, and average total cost.
Fixed costs: Costs that cannot be changed in the short run
Variable costs: Costs that vary with the number of labor units and production levels, primarily driven by labor and material usage
Total costs: Dependent upon number of labor units
Marginal Product of Labor (MPL): Additional output produced by adding one more labor unit, difference in total output when increasing labor units
Initially increases due to specialization
Eventually decreases due to diminishing returns (e.g., overcrowding, waiting for supplies).
Marginal Cost: Costs incurred for producing an additional unit of output, change in total cost divided by change in output
Decreases initially as efficiency increases with specialization
Increases after reaching diminishing returns
Average Variable Cost (AVC): Variable cost divided by total output
Average Fixed Cost (AFC): Fixed cost divided by total output
AVC and ATC initially decrease due to economies of scale (efficient allocation of variable resources), then increase after a certain output level.
AFC continues to decrease as fixed costs are spread over more units.
The point where marginal costs intersect average variable cost indicates a change in direction for the Average Variable Cost (AVC).
Average Fixed Cost continues to decrease as output increases.