Econ 203 Lab #2 Section A: Test Your Understanding. True or False? 1) The long run refers to a period when all inputs are variable and none is fixed.

Transcription

1 Econ 203 Lab #2 Section A: Test Your Understanding February 15, 2016 True or False? 1) The long run refers to a period when all inputs are variable and none is fixed.

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4 Long Run Production - Returns to Scale In the long run, all factors of production are variable. How the output of a business responds to a change in factor inputs is called returns to scale. Numerical example of long run returns to scale Units of Capital Units of Labour Total Output % Change in Inputs % Change in Output Returns to Scale Increasing Increasing Constant Decreasing When we double the factor inputs from (150L + 20K) to (300L + 40K) then the percentage change in output is 150% - there are increasing returns to scale. When the scale of production is changed from (600L + 80K) to (750L + 100K) then the percentage change in output (13%) is less than the change in inputs (25%) implying a situation of decreasing returns to scale. Increasing returns to scale occur when the % change in output > % change in inputs Decreasing returns to scale occur when the % change in output < % change in inputs Constant returns to scale occur when the % change in output = % change in inputs

5 The nature of the returns to scale affects the shape of a business s long run average cost curve. Finding an optimal mix between labour and capital In the long run businesses will be looking to find an output that combines labour and capital in a way that maximises productivity and therefore reduces unit costs towards their lowest level. This may involve a process of capital-labour substitution where capital machinery and new technology replaces some of the labour input. In many industries over the years we have seen a rise in the capital intensity of production - good examples include farming, banking and retailing.

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7 Another:

8 2) The average product of an input is the addition to the total output due to the addition of the last unit of input used, the quantity of other inputs used being held constant.

9 Best Answer - Chosen by Voters Marginal product is the additional output that will be forthcoming from an additional worker, assuming that other inputs are constant. Average product is output per worker, or the total output divided by the number of workers. Marginal product is the addition to the total product when an additional unit of variable input is employed with fixed quantities of other inputs. Average Product is the Total Product/output per variable input

10 AVERAGE PRODUCT: The quantity of total output produced per unit of a variable input, holding all other inputs fixed. Average product, usually abbreviated AP, is found by dividing total product by the quantity of the variable input. Average product, which occasionally goes by the alias average physical product (APP), is one of two measures derived from total product. The other is marginal product. Average product is the per unit production of a firm. Conceptually, it is simply the arithmetic mean of total product calculated for each variable input over a whole range of variable input quantities. Average product is generally considered less important than total product and marginal product in the analysis of short-run production. The formula for specifying and calculating average product from total product is given as:

11 average product = total product variable input False

12 3. The law of diminishing marginal returns is not applicable to cases in which there is a proportional increase in all inputs.

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14 In economics, diminishing returns (also called diminishing marginal returns) is the decrease in the marginal (per-unit) output of a production process as the amount of a single factor of production is increased, while the amounts of all other factors of production stay constant. The law of diminishing returns (also law of diminishing marginal returns or law of increasing relative cost) states that in all productive processes, adding more of one factor of production, while holding all others constant ("ceteris paribus"), will at some point yield lower per-unit returns. [1] The law of diminishing returns does not imply that adding more of a factor will decrease the total production, a condition known as negative returns, though in fact this is common.

15 Answer: True

16 Section A: 1. Sketch the graph of a "standard " shortrun production function, and identify on it the points where the average product peaks(a), the marginal product peaks(b), the marginal product reaches zero(c), and the average and marginal product intersect(d).

17 Ans: The average product of labour peaks at the output level where the ray from the origin is tangent to the total product curve, where it equals the marginal product of labour (at A=D). The marginal product peaks at the output level corresponding to the inflection point on the total product curve (at B), and the marginal product reaches zero when the total product peaks (at C).

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20 Question 2: Which of the following production functions exhibits increasing returns to scale? A) Q = K 1/2 L l/2 B) Q = K l/2 L 2/3 C) Q = K l/4 L l/3 D) Q = K/L (Hint: Add up the exponents.)

21 Ans: B

22 Question 3: A representative isoquant for perfect complements is A) L-shaped. B) a straight line. C) a ray passing through the origin. D) concave. E) not necessarily any of the above.

23 Example of an isoquant map with two inputs that are perfect complements.

24 Ans: A

25 Question 4: The production function for calculators is Q = 12L 2 - L 3, where Q is in calculators /day and L is in labour-days /day. Show all your work for the following questions. Give the equation for the marginal product of labour (MPL), and its value when L = 6 labour-days/day.

26 Ans: Q = 12L 2 - L 3 Q/ L=MPL = 24L - 3L 2, 24(6)-3(6*6)=36 which equals 36 calculators/labour-day when L = 6 labourdays/day.

27 Question 5 : The production function for gravel is Q = 10L 1/2 K 1/2 (where Q is in units, L is in labour-days, and K is in machine-days). With L on the horizontal axis and K on the vertical axis, give the formula for the MRTS of the relevant isoquant for any given combination of inputs (K, L), and give the value of the MRTS when L= 9 labour-days and K = 16 machine-days.

28 MRTS 1/ 2 1/ 2 MP L L K K MP 5 K L K L 1/ 2 1/ (negative value)

29 1. If equal increments of a variable input are combined with a fixed input, A) the increments to output will eventually increase. B) the additions to output will be constant. C) total cost will eventually decrease. D) output will eventually increase at a decreasing rate.

30 Ans: D

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33 Question: The marginal product of a variable input is A) zero at the point of diminishing returns. B) the change in average product that occurs when the variable input is increased by one unit. C) the change in the total product that occurs in response to a unit change in the variable input. D) the second derivative of the total product function. E) more than one of the above.

34 Ans: C

35 3. The average product of a variable input A) decreases at an increasing rate. B) is the sum of the individual marginal cost curves. C) is the change in the total product that occurs when the variable input increases by one unit. D) is the total product divided by the quantity of the variable input. E) necessarily increases initially and subsequently diminishes.

36 Ans: D

37 4. (3 marks) SuperBlast Cola ( the soft drink with 10 times the regular amount of caffeine, for those all-night studythons! ) can be produced using either of two production processes: Q1 = LK 1/2 or Q2 = L 3/4 K 3/4. a. For each production process, state whether it is characterized by constant, increasing, or decreasing returns to scale, and whether it displays constant, increasing, or diminishing marginal productivity of labour and of capital.

38 Ans: a. Both production processes are characterized by increasing returns to scale: doubling both inputs increases output by a factor of 2 3/2, or 2 2 ( 2.828). Q1 has a diminishing MPK (MPK =.5LK -1/2 ) and a constant MPL (MPL = K), while Q2 has a diminishing MPK (MPK =.75L 3/4 K -1/4 ) and a diminishing MPL (MPL =.75K 3/4 L -1/4 ).

39 b. Calculate Q1 and Q2 when L = K = 1 and when L = K = 16. When L = K = 1, then Q1 = Q2 = 1 unit of SuperBlast, and when L = K = 16, then Q1 = Q2 = 64 units of SuperBlast.

40 c. Give the formulas for Q1 and Q2 as functions of L when K = 16, and then calculate the formulas for MPL in each case. For what values of L is Q1 < Q2? For what values of L is Q1 = Q2? For what values of L is Q1 > Q2? If K = 16 units, then Q1 = 4L, while Q2 = 8L 3/4. Hence for process 1, MPL = 4, while for process 2, MPL = 6L -1/4. Q1 < Q2 for 0 < L < 16 labour-units, Q1 = Q2 for L = 16 labour-units, and Q1 > Q2 for L > 16 labour-units.

41 Question: Ace Dry Cleaning, Inc. currently employs 26 labourdays per day in its pants division, along with its fixed plant and equipment. Pants are dry-cleaned using one of two processes: Process 1, which is characterized by the average product of labour (AP L ) equation (AP L ) 1 = 40 - L 1, and Process 2, with equation (AP L ) 2 = L 2. Give the equations for MP L for each process. Ans: TP L1 =40L-L 2 (MP L ) 1 = 40-2L 1 TP L2 =30L-0.5L 2 (MP L ) 2 = 30 - L 2. AP = TP/L MP= dtp/dl TP= AP*L