Intermediate Microeconomics · free preview
Profit Functions and Comparative Statics
The optimized profit is itself a function of prices, convex in output price, whose price derivatives are supply and whose wage derivatives are conditional demands, the envelope logic tying every firm-side object into one dual system, closed by comparative-statics signs.
1. The profit function
The profit function
2. Envelope derivatives
Envelope derivatives
3. Comparative-statics signs
Comparative-statics signs
4. The module closed and ahead
The module closed and ahead
5. The profit function's shape
How does the profit function behave in the wage?
6. Hotelling's lemma
What exactly does Hotelling's lemma state about the profit function's derivatives?
7. Checking the worked function
For pi equal to p squared over 4w, what is the p-derivative at (10, 2)?
8. No Giffen inputs
Why can a firm's factor demand never slope upward in its own wage?
9. The wage derivative
Compute the derivative of p squared over 4w with respect to w at (10, 2), and write the number.
10. Profit at the worked point
Evaluate p squared over 4w at p of 10 and w of 2, and write the number.
11. Profit at the higher price
The profit function is pi equal to p squared over 4w. What is profit at p of 12 and w of 2?
12. Supply read off the envelope
By Hotelling's lemma, what is the firm's supply at p of 12 and w of 2?
13. A dearer wage's bite
The profit function is pi equal to p squared over 4w. What is profit at p of 10 and w of 4?
14. The factor demand, enveloped
By the lemma's other half, minus the w-derivative of profit gives the factor demand. What is it at (10, 2)?
15. Profit at the lower price
For pi equal to p squared over 4w, compute profit at p of 8 and w of 2, and write the number.
16. Supply at the lower price
Compute the p-derivative of pi, p over 2w, at p of 8 and w of 2, and write the number.
Practice this interactively
Free account · instant grading · spaced review that schedules itself.
Start this course for free