Intermediate Microeconomics · free preview
The Family of Cost Curves
From a total cost function come marginal cost, average variable cost, and average total cost, with fixed cost generating the falling AFC, and the geometric law that marginal crosses both averages exactly at their minima, the whole family drawn from one cubic.
1. Slicing the cost function
Slicing the cost function
2. The crossings
The crossings
3. Areas and totals
Areas and totals
4. Reading the family at a price
Reading the family at a price
5. Deriving the family
For c of q equal to q cubed minus 6 q squared plus 16 q plus 36, what is AVC?
6. The crossing law
In this cubic cost family, where exactly does the MC curve cross the AVC curve?
7. The AFC component
What does average fixed cost look like and why?
8. Profit at 16
At price 16 the firm supplies q of 4. What is its profit?
9. AVC minimum
Minimize AVC equal to q squared minus 6 q plus 16. What is the minimum value? Write the number.
10. The ATC bottom
Compute ATC at q equal to 4, that is 16 minus 24 plus 16 plus 36 over 4, and write the number.
11. The fixed spread
For the cubic family, what is average fixed cost at q of 4?
12. The efficient scale
Where does average total cost bottom out for this cubic family?
13. The variable bill
What is total variable cost at q of 4 for this family?
14. The crossing verified
At q of 3 where AVC is minimized, what does the MC curve read?
15. Average fixed cost at four
For the cubic family with fixed cost 36, compute average fixed cost at q of 4, and write the number.
16. Average total cost at two
For the cubic family, compute ATC at q of 2, that is 8 minus 24 plus 32 plus 36, all over 2, and write the number.
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