Production functions - linear, homogeneous, Cobb-Douglas, CES production functions - short run and long run cost curves, derivation of cost functions from production functions, least cost combination of factor inputs - One Line Questions

1. If a production function is Q = f(L, K), what is the marginal product of labor (MPL)? — ∂Q/∂L
2. In a Cobb-Douglas production function Q = L^0.5 * K^0.5, what is the elasticity of substitution? — 1
3. If P_L = $5, P_K = $10, and the production function is Q = L*K, what is the MRTS when L=10 and K=5? — 0.5
4. The relationship between the production function and cost function is that the cost function is derived by minimizing cost subject to: — A given output level
5. What does the law of diminishing marginal returns state? — Adding more of one input, while holding others fixed, will eventually increase total output at a decreasing rate.
6. The short-run cost curves (SRAC, SAC, SMC) are derived from the short-run production function where: — One factor is fixed
7. What is the primary characteristic of a short-run production period? — At least one input is fixed
8. The short-run cost curves are derived from the production function assuming: — At least one input is fixed
9. When does a firm experience economies of scale in the long run? — As output increases, LRAC decreases
10. In the long run, how are production inputs treated? — All inputs are variable
11. Which cost curve is typically U-shaped in the short run? — Average Variable Cost (AVC)
12. If the price of labor (P_L) increases while the price of capital (P_K) stays the same, the isocost line will: — Become steeper
13. Which production function is characterized by fixed proportions, meaning inputs must be used in a specific ratio? — Leontief (Fixed Proportions)
14. A production function Q = 5L + 10K represents: — Linear production function with perfect substitutability
15. What does the isoquant represent in production theory? — Combinations of inputs that yield the same level of output
16. An isocost line represents: — Combinations of inputs that result in the same total cost
17. Which characteristic defines a linear production function? — Constant returns to scale
18. When marginal product (MP) is positive but decreasing, total product (TP) is: — Increasing at a decreasing rate
19. If a firm is operating on the downward-sloping portion of its LRAC curve, it is experiencing: — Economies of scale
20. In the long run, if a firm doubles all its inputs and output more than doubles, it experiences: — Increasing returns to scale
21. Which of the following is NOT a factor influencing the shape of the long-run average cost curve? — Law of diminishing marginal returns
22. A firm is producing at the least-cost combination of inputs. If the price of labor falls, the firm should: — Employ more labor and less capital
23. Total Cost (TC) in the short run is the sum of: — Fixed Cost (FC) and Variable Cost (VC)
24. Which of the following is a property of a homogeneous production function of degree 'n'? — If all inputs are multiplied by 'x', output is multiplied by 'x^n'
25. A production function is said to be homogeneous of degree one if it exhibits: — Constant returns to scale
26. In the Cobb-Douglas production function Q = A * L^α * K^β, if α + β = 1, what kind of returns to scale does the function exhibit? — Constant returns to scale
27. A firm produces 100 units using 10 units of labor and 5 units of capital. If it doubles its inputs to 20 units of labor and 10 units of capital, and output increases to 150 units, what returns to scale are observed? — Decreasing returns to scale
28. If a CES production function has a substitution elasticity of 0.5, this implies: — Inputs are imperfect substitutes, closer to complements
29. The optimal (least cost) combination of inputs for a given output level occurs where the isoquant is tangent to the: — Isocost line
30. In the short run, as more of a variable input is added to a fixed input, what eventually happens to marginal product? — It eventually diminishes
31. The Marginal Cost (MC) curve intersects the Average Variable Cost (AVC) curve at: — Its lowest point
32. The Cobb-Douglas production function is typically represented as Q = A * L^α * K^β. What does 'A' represent in this equation? — Technological progress
33. Which production function is a generalization of Cobb-Douglas and Leontief production functions? — CES production function
34. Which cost curve is always downward sloping? — Average Fixed Cost (AFC)
35. Average product (AP) is maximized when: — Marginal product (MP) equals average product (AP)
36. The 'least cost combination of factor inputs' refers to the point where: — Total cost is minimized for a given output level
37. The slope of an isoquant is known as the: — Marginal rate of technical substitution (MRTS)
38. The point where the MC curve intersects the ATC curve is the: — Minimum point of ATC
39. The condition for the least cost combination of factor inputs is often expressed as MPL / P_L = MPK / P_K, where P_L and P_K are prices of labor and capital. This can be rewritten as: — MPL / MPK = P_K / P_L
40. The Constant Elasticity of Substitution (CES) production function allows for: — A substitution elasticity other than one
41. The total product curve in the short run typically shows: — Output increasing at an increasing rate, then at a decreasing rate
42. A firm's cost function, C(Q), relates: — Total cost to the level of output
43. Long-run average cost (LRAC) is the envelope of which curves? — Short-run average total cost (SRATC) curves
44. What does the exponent 'α' represent in the Cobb-Douglas production function Q = A * L^α * K^β? — The elasticity of output with respect to labor
45. The shape of the short-run marginal cost (MC) curve is primarily determined by: — The law of diminishing marginal returns
46. The expansion path for a firm shows: — The least cost combination of inputs for each output level
47. What does a production function fundamentally represent in economics? — The maximum output achievable with given inputs
48. Deriving cost functions from production functions involves substituting input prices into the: — Input combination that yields a given output at minimum cost
49. If the marginal product of labor (MPL) is 20 and the marginal product of capital (MPK) is 30, and the price of labor (P_L) is $10 and the price of capital (P_K) is $15, is the firm using the least cost combination of inputs? — No, because MPL/MPK != P_L/P_K
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