Intermediate Microeconomics · free preview

Fixed Proportions and Perfect Substitutes

The two extreme technologies bracket all others, fixed proportions f equals min of ax1 and bx2 with L-shaped isoquants where no substitution is possible, and perfect substitutes f equals ax1 plus bx2 with straight isoquants where substitution is constant.

1. Fixed proportions

Fixed proportions

2. Perfect substitutes

Perfect substitutes

3. Marginal products at the poles

Marginal products at the poles

4. Choosing the poles in practice

Choosing the poles in practice

5. The binding input

For f equal to min of 2x1 and x2, what is output at (10, 12)?

6. The kink line

Where do the kinks of the isoquants of f equal min of 2x1 and x2 lie?

7. Perfect substitutes TRS

For f equal to 2x1 plus 3x2, what is the TRS and how does it vary along an isoquant?

8. Substitution and prices

Why do kinked technologies ignore relative input prices for the mix?

9. Linear output

For f equal to 2x1 plus 3x2, compute output at (5, 4), and write the number.

10. Kink output

For f equal to min of 2x1 and x2, compute output at the kink bundle with x1 equal to 3 and x2 equal to 6, and write the number.

11. The short arm again

For f equal to min of 2x1 and x2, what is output at the bundle (4, 10)?

12. A linear corner

For f equal to 2x1 plus 3x2, what is output at the bundle (0, 7)?

13. The tie on the input side

For f equal to 2x1 plus 3x2 with input prices w1 of 2 and w2 of 3, which input mix does a cost-minimizer choose?

14. Excess capacity wasted

For f equal to min of 2x1 and x2 with x2 fixed at 6, x1 rises from 3 to 5. What happens to output?

15. Output off the kink

For f equal to min of 2x1 and x2, compute output at the bundle (4, 10), and write the number.

16. Linear output on the axis

For f equal to 2x1 plus 3x2, compute output at the bundle (0, 7), and write the number.

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