Eco 550 Week 4 Chp 7 & 8 Checking Your Understandinf

Chapter 7

1. a. L TPX (=Q) MPX = ΔQ/ΔX APX = Q/X

0 0 --- ---

1 3 3 3.00

2 6 3 3.00

3 16 10 5.33

4 29 13 7.25

5 43 14 8.60

6 55 12 9.17

7 58 3 8.29

8 60 2 7.50

9 59 −1 6.56

10 56 −3 5.60

B.

C. Stage I: 0 − 6 APX is increasing

Stage II: 6+ − 8+ TPX ≥ 0

Stage III: 8+ − ∞ MPX < 0

6. Consider the following short-Run production function (where L=Variable input, Q=output): Q=10L- 0.5L2

A. Q = 10L −0.5L2

= 100-10L

B. 10L = 10

C. L* = 8

8. Based on the production function parameter estimates reported in Table 7.4:

A. Q = 2.5 L.5C.5

L increases by 10% to L' = 1.1L

Q' = 2.5(1.1L).5C.5

Q' = (1.1).5[2.5L.5C.5]

Q' = 1.0488Q

The ooutput of Q’ increases by 4.88%.

B. C' = 1.25C, then Q' = 2.5L.5 (1.25C).5

Q' = (1.25).5 [2.5L.5C.5]

Q' = 1.118Q, output Q' increases by 11.8%.

C. Both L and C increase

= 1.2C, Q' = 2.5(1.2L).5(1.2C).5

Q' = (1.2).5 (1.2).5 [2.5L.5C.5]

Q' = (1.0954) (1.0954) Q

Q' = 1.20Q

Q' increased by 20% and the exponent is 1

9. A. (i). EL = β1 = .45; (ii). EF = β2 = .20; (iii). EB = β3 = .30.

B. EL = %ΔQ/%ΔL = .45. Ir %ΔL = .02, %ΔQ = .45 (.02) = .009 (.9%).

C EB = %ΔQ/%ΔB = .30. If %ΔB = −.03, %ΔQ = .30(−.03) = -.009 (-.9%).

D. β1 + β2 + β3 = .45 + .20 + .30 = .95

Decreasing Returns to Scale, due to the sum of the exponents are less than 1.

E. As Technical progress advances it will cause a change in the process used in production over time. An example of this is factory improvement, better machines, capable of more processes and faster production could result in a greater output meaning more garments produced in the same amount of time, this would be true with the number of operators, production cost and factory size remaining the same. Replacement of older machines...