Intermediate Microeconomics · free preview
Inputs, Outputs, and Isoquants
A production function maps input bundles to maximal output, the isoquant is its level curve, and well-behaved technologies are monotone and convex, free disposal and feasible averaging.
1. The production function
The production function
2. Marginal products
Marginal products
3. The technical rate of substitution
The technical rate of substitution
4. The short run and the long run
The short run and the long run
5. What the function means
What does the production function y equals f of x1 and x2 record?
6. Monotonicity and convexity
What do monotonicity and convexity of the technology mean economically?
7. Computing marginal products
For f equal to the square root of x1 times x2 at (4, 9), what are the marginal products?
8. The TRS reading
The TRS at (4, 9) is 2.25. What does the number say?
9. Output at the bundle
For f equal to x1 to the one half times x2 to the one half, compute output at (4, 9), and write the number.
10. The substitution rate
Compute the TRS at (4, 9) as MP1 over MP2, and write the number.
11. The first marginal product
For f equal to the square root of x1 x2 at the bundle (4, 9), what is the marginal product of input one?
12. The other margin
At the same bundle (4, 9), what is the marginal product of input two?
13. The symmetric point
At the bundle (9, 4), the same output 6 is produced. What is the TRS there?
14. Membership on the isoquant
Which bundle does NOT lie on the isoquant of output 6, that is x1 x2 equals 36?
15. TRS at the mirror
For the square-root technology at the bundle (9, 4), compute the TRS as a fraction, and write it.
16. A margin farther out
For the same technology at the bundle (16, 9), compute the marginal product of input one, and write the number with three decimals.
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