Eco 550 Check Your Understanding Week 4 (Answers)
Check Your Understanding Week 4
Chapter 7: Problems 1, 6, 8, and 9
Chapter 7
Production Economics
___________________________
Solutions to Exercises
1. Deep Creek Mining Company:
Complete the table.
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 increasing Stage II: 6+ − 8+ MPX ≥ 0 Stage III: 8+ − ∞ MPX < 0
6. a. Q = 10L − .5L2 MPL = 10 − 1.0L MRQ = Price = $10 MRPL = (10 − 1.0L)($10) = $100 − $10L
b. MFCL = $20
c. The optimal level of the variable input occurs where: MRPL = MFCL 100 − 10L = 20, so L* = 8
9. a. (i). EL = β1 = .45; (ii). EF = β2 = .20; (iii). EB = β3 = .30.
b. EL = %ΔQ/%ΔL = .45. If %ΔL = .02, %ΔQ = .45(.02) = .009, or .9%.
c. EB = %ΔQ/%ΔB = .30. If %ΔB = −.03, %ΔQ = .30(−.03) = -.009 or -.9%.
d. β1 + β2 + β3 = .45 + .20 + .30 = .95, this is Decreasing Returns to Scale, because the sum of the exponents is less than 1.
e. Technical progress causes the production process to change over time. For example, wider roads and improved traffic control systems may result in increased output (i.e., bus miles) even though the number of buses (i.e., capital input) and drivers (i.e., labor input) remains constant. Likewise, the replacement of older buses with new models may increase output since the new buses may be faster and more maneuverable. Finally, as the experience level of the bus drivers increases over time, output may increase even though the number of drivers remains constant
o Chapter 8: Problems 2(a), 4, and 6(a)
2. Howard Bowen’s cotton farm analysis appears below. a. Accounting profits:
Revenues $5,000,000
Less: Variable operating costs 4,500,000
Less: Depreciation 40,000
Chapter 7: Problems 1, 6, 8, and 9
Chapter 7
Production Economics
___________________________
Solutions to Exercises
1. Deep Creek Mining Company:
Complete the table.
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 increasing Stage II: 6+ − 8+ MPX ≥ 0 Stage III: 8+ − ∞ MPX < 0
6. a. Q = 10L − .5L2 MPL = 10 − 1.0L MRQ = Price = $10 MRPL = (10 − 1.0L)($10) = $100 − $10L
b. MFCL = $20
c. The optimal level of the variable input occurs where: MRPL = MFCL 100 − 10L = 20, so L* = 8
9. a. (i). EL = β1 = .45; (ii). EF = β2 = .20; (iii). EB = β3 = .30.
b. EL = %ΔQ/%ΔL = .45. If %ΔL = .02, %ΔQ = .45(.02) = .009, or .9%.
c. EB = %ΔQ/%ΔB = .30. If %ΔB = −.03, %ΔQ = .30(−.03) = -.009 or -.9%.
d. β1 + β2 + β3 = .45 + .20 + .30 = .95, this is Decreasing Returns to Scale, because the sum of the exponents is less than 1.
e. Technical progress causes the production process to change over time. For example, wider roads and improved traffic control systems may result in increased output (i.e., bus miles) even though the number of buses (i.e., capital input) and drivers (i.e., labor input) remains constant. Likewise, the replacement of older buses with new models may increase output since the new buses may be faster and more maneuverable. Finally, as the experience level of the bus drivers increases over time, output may increase even though the number of drivers remains constant
o Chapter 8: Problems 2(a), 4, and 6(a)
2. Howard Bowen’s cotton farm analysis appears below. a. Accounting profits:
Revenues $5,000,000
Less: Variable operating costs 4,500,000
Less: Depreciation 40,000