Intermediate Microeconomics · free preview
Cost Minimization
The firm producing y at least cost solves min w1 x1 plus w2 x2 on the isoquant, tangency TRS equals w1 over w2, and the solution defines conditional factor demands and the cost function c of w and y, the dual of profit maximization.
1. The problem and its tangency
The problem and its tangency
2. Conditional demands and the cost function
Conditional demands and the cost function
3. Corners and kinks
Corners and kinks
4. Cost minimization and profit maximization
Cost minimization and profit maximization
5. The tangency condition
The interior cost-minimizing bundle satisfies which condition?
6. The worked solution
Square-root technology, y of 12, wages 3 and 12. What is the conditional demand for x1?
7. The cost function's content
What exactly does the cost function c of w and y record?
8. Corners under substitutes
Perfect substitutes with w1 over a above w2 over b. Which bundle is cheapest for output y?
9. Total cost at the optimum
For the worked problem, compute the minimized cost 3 times 24 plus 12 times 6, and write the number.
10. Average cost
Divide the minimized cost 144 by the output 12, and write the average cost.
11. The other conditional demand
In the worked cost-minimization, y of 12 with wages 3 and 12, x1 is 24. What is x2?
12. The dollar split
At the worked optimum, how do the dollars split between the two inputs?
13. Doubling the target
The same firm now must produce y of 24 instead of 12, wages unchanged. What is the minimized cost?
14. Equal wages reshuffle
Suppose instead both wages equal 3. What is the cheapest way to produce y of 12?
15. Cost at doubled output
With wages 3 and 12, compute the minimized cost of producing y of 24, and write the number.
16. Average cost unchanged
Under the same technology and wages, compute average cost at y of 24, that is 288 over 24, and write the number.
Practice this interactively
Free account · instant grading · spaced review that schedules itself.
Start this course for free