Intermediate Microeconomics · free preview
Returns to Scale
Scaling all inputs by t scales output by more, exactly, or less than t, increasing, constant, or decreasing returns, a long-run property distinct from diminishing marginal product, and the Cobb-Douglas exponents sum to t's power.
1. The scaling experiment
The scaling experiment
2. The Cobb-Douglas exponent rule
The Cobb-Douglas exponent rule
3. Scale is not marginal product
Scale is not marginal product
4. Where returns come from
Where returns come from
5. The scaling test
Doubling inputs from (4, 9) to (8, 18) in f equal to x1 to the one half x2 to the one half moved output from 6 to 12. What is the classification?
6. The exponent rule
For f equal to x1 to the 0.3 times x2 to the 0.3, what are the returns to scale?
7. The designated confusion
A technology shows diminishing marginal product of every input. What follows about returns to scale?
8. Economic sources
What economic story lies behind increasing returns to scale?
9. The DRS growth factor
For the sum 0.6 technology, compute 2 to the power 0.6, the output growth factor when inputs double. Write the number to two decimals.
10. Verifying exact doubling
For f equal to x1 to the one half x2 to the one half, compute f of (8, 18), and write the number.
11. A decreasing-returns family
For f equal to x1 to the 0.4 times x2 to the 0.5, what are the returns to scale?
12. The increasing extreme
For f equal to x1 times x2, what happens when both inputs double?
13. A moderate sum
For a technology with exponent sum 0.75, by what factor does output grow when inputs double?
14. Tripling under constant returns
For f equal to x1 to the one half x2 to the one half, output at (4, 9) is 6. What is output at (12, 27)?
15. Growth factor at sum 0.9
For an exponent sum of 0.9, compute 2 to the power 0.9, the output growth factor per input doubling, rounded to two decimals, and write the number.
16. Tripling the inputs
For f equal to x1 to the one half x2 to the one half, compute f of (12, 27), and write the number.
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