Unit 5: Production and the Costs of the Firm
How a factory's output translates into a family of cost curves, and why every curve eventually turns upward.
8 topics · 27 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
The Production Function and Total Product
- How it worksHow does a production function turn hours of labor, holding the ovens fixed, into total loaves of bread?
- How it worksHow does the total product curve rise, then bend, as more workers are added to a fixed kitchen?
- Going furtherWhat happens to total product as even more workers are packed into the same fixed-size kitchen?
Your turn1 of 2
A firm's short-run production function is TP = 35 times L minus 1.15 times L squared, where L is the number of workers. What is total product at 12 workers?Marginal and Average Product and Diminishing Returns
- How it worksHow does marginal product measure the extra output from adding one more worker to a fixed amount of capital?
- Worked exampleFind the marginal product of the fourth worker when three workers produce 30 units and four workers produce 36 units.
- Common mistakeWhy doesn't diminishing marginal returns mean that total output is actually falling?
Your turn1 of 2
A team of workers producing 30 units total hires one additional worker, raising total output to 48 units. What is the marginal product of that additional worker?Fixed and Variable Costs in the Short Run
- How it worksHow do fixed costs and variable costs combine into a firm's total cost at every output level?
- Worked exampleFind total cost at 50 units of output when fixed cost is 200 dollars and variable cost is 6 dollars per unit.
- Going furtherWhat happens to a firm's total cost curve when its fixed cost rises but variable cost per unit stays the same?
Your turn1 of 2
Find total cost at 76 units of output when fixed cost is 239 dollars and variable cost is 8 dollars per unit.Marginal Cost and Average Cost Curves
- How it worksHow does diminishing marginal returns in production translate directly into a rising marginal cost curve?
- Worked exampleFind the marginal cost of the tenth unit when total cost at 9 units is 90 dollars and at 10 units is 105 dollars.
- How it worksHow do average fixed, average variable, and average total cost curves each trace their own U-shape?
- Common mistakeWhy isn't marginal cost the same thing as average total cost at every level of output?
Your turn1 of 2
Total cost is 129 dollars at a certain output, and rises to 196 dollars when one more unit is produced. What is the marginal cost of that unit?Why Marginal Cost Crosses Average Cost at Its Minimum
- How it worksHow does that same pulling logic force marginal cost to cross average total cost exactly at its lowest point?
- Worked exampleFind whether average total cost is rising or falling when marginal cost is 8 dollars and average total cost is 10 dollars.
- Common mistakeWhy doesn't marginal cost crossing average cost at its minimum happen at some other random output level?
- Ties togetherHow does marginal cost crossing both average variable and average total cost connect their two separate minimum points?
Your turn1 of 2
By how many dollars does marginal cost exceed average total cost when marginal cost is 16 dollars and average total cost is 11 dollars?Costs in the Long Run and the LRAC Curve
- How it worksHow does a firm pick, for each output level, whichever plant size gives it the lowest possible average cost?
- How it worksHow does tracing the lowest cost across every plant size build the long-run average cost curve as an envelope?
- Ties togetherHow does the long-run average cost curve relate to the individual short-run cost curves it's built from?
Your turn1 of 2
Building a plant of size A costs 339 dollars in fixed cost plus 9 dollars per unit produced, while a plant of size B costs 795 dollars in fixed cost plus 3 dollars per unit. At what output level do the two plants cost the same total amount to run?The Relationship Between Short-Run and Long-Run Costs
- How it worksHow does a short-run average cost curve sit tangent to the long-run curve at only one output level?
- How it worksHow does every short-run curve stay on or above the long-run envelope curve, never below it?
- Ties togetherHow does this tangency relate to a firm choosing to build a bigger plant as it expects to grow?
Your turn1 of 2
A firm's short-run average cost curve touches its long-run average cost curve at exactly one output level and lies above the long-run curve everywhere else. What does this describe?Economies and Diseconomies of Scale
- How it worksHow does specialization and bulk buying let long-run average cost fall as a firm scales up production?
- Worked exampleFind whether a firm has economies of scale when doubling output from 100 to 200 units drops average cost from 10 to 8 dollars.
- Going furtherWhat happens to long-run average cost once a firm grows so large that coordination costs start to dominate?
- Common mistakeWhy isn't a bigger firm always a cheaper-per-unit firm no matter how large it grows?
Your turn1 of 2
A firm doubles every input, and output rises from 108 to 232 units while average cost falls from 15 dollars to 5 dollars. By what percent did average cost change?