Chapter 5 Homework
10. Use the table to answer one question about marginal physical product (MPP). LABOR INPUT: 0/1/2/3/4/5/6/7/8 OUTPUT: 0/15/34/44/48/50/51/51/47 MPP: --/15/19/10/4/2/1/0/-4 b.If investment in new machinery doubles the productivity of every worker, the MPP of the fifth worker will be___pairs of jeans.
4 The marginal physical product (MPP) of the fifth worker is 2 pairs of jeans. MPP of the fifth worker = (total output with the fifth worker − total output of fourth worker) ÷ (one more worker) = (50 − 48) ÷ 1 = 2 If productivity for this worker doubled, productivity would increase to 4 pairs of jeans (= 2 × 2).
8. Refer to the cost table below and answer two questions about profit. RATE OF OUTPUT: 0/10/15/20/30/40/50/51 FC: 120 VC: 0/85/125/150/240/350/550/633 TC: 120/205/245/270/360/470/670/753 ATC: 20.50/16.33/13.50/12.00/11.75/13.40/14.76 Compute total profits at a price of $15 per pair of jeans and output ofa. (A) 40 pairs (B) 50 pairs
You can calculate profit using two different methods depending on the information available to you. Total profit is equal to total revenue minus total cost (Profit = TR − TC). Total revenue is price multiplied by quantity (TR = p × q). Total cost is given in the table. OR Total profit is equal to the quantity sold multiplied by the difference between price and average total cost (Profit = q × (p − ATC)). All of this information is given in the table.a. (A) 130 (a) Total profit is $130 when price is equal to $15 and output is equal to 40. Profit = TR − TC = (p × q) − TC = ($15 × 40) − $470 = $600 − $470 = $130 Profit = q × (p − ATC) = 40 × ( $15.00 − $11.75) = $130 (B) 80 (b) Total profit is $80 when price is equal to $15 and output is equal to 50. Profit = TR − TC = (p × q) − TC = ($15 × 50) − $670 = $750 − $670 = $80 Profit = q × (p − ATC) = 50 × ($15.00 − $13.40) = $80
9. Use the following information to answer three questions about accounting and economic costs. Suppose a company incurs the following costs: LABOR: $800 EQUIPMENT: $400 MATERIALS: $300 The company owns the building, so it doesn't have to pay the usual $900 in rent.a. (A) What is the total accounting cost? (B) What is the total economic cost? (C) What would the new accounting and economic costs be if the company sold the building and then leased it back? New total accounting cost?/New total economic cost?
(A) 1500 (a) Accounting costs include dollar costs only (those explicit costs) and ignore any resource use that doesn't result in an explicit dollar cost. These explicit costs include the checks written for the labor, equipment, and materials, which total to $1,500 (= $800 + $400 + $300). (B) 2400 (b) Economic costs include the value of all resources used to produce a good or service. This includes all explicit costs plus implicit costs, which total to $2,400 (= $1,500 explicit costs totaled in part a + $900 implicit cost in rent). (C) 2400/2400 (c) Accounting costs would increase by the amount of the lease because the lease payment is now an explicit dollar outlay. Accounting costs now total to $2,400 (= $800 + $400 + $300 + $900). Economic costs already include the true costs of the building use and would therefore not change.
5. Given the following production function for the mythical Tight Jeans Corporation, calculate the marginal physical product, graph the production function and marginal physical product on two separate graphs, then answer three questions about marginal productivity. A) Calculate the marginal physical product. B) Graph the production function. C) Illustrate marginal physical product (MPP). At what level of employment does: D) the law of diminishing returns become apparent? E) MPP hit zero? F) MPP become negative?
(A) LABOR INPUT: 0/1/2/3/4/5/6/7/8 OUTPUT: 0/10/36/56/68/74/76/76/74 MPP: --/10/26/20/12/6/2/0/-2 (a) The marginal physical product is the change in output when one more worker is hired. It is calculated as the change in output divided by the change in the number of workers [= (Q2 − Q1) ÷ (L2 − L1)]. For example, when one worker is hired the marginal physical product is 10 [= (10 − 0) ÷ (1 − 0)], when a second worker is hired the marginal physical product is 26 [= (36 − 10) ÷ (2 − 1)], and so on. (b) The production function is plotted with the quantity of output on the vertical axis and the number of workers on the horizontal axis. One point along the production function is 10 pairs of jeans and 1 worker (10, 1). A second point along the production function is 36 pairs of jeans and 2 workers (36, 2). The rest of the production function is plotted in the same manner. (c) The marginal physical product curve is plotted with marginal physical product on the vertical axis and the number of workers on the horizontal axis. One point along the MPP curve is 10 pairs of jeans and 1 worker (10, 1). A second point along this curve is 26 pairs of jeans and 2 workers (26, 2). (D) worker 3 (d) The law of diminishing returns states that the marginal physical product (MPP) of a variable input declines as more of it is employed with a given quantity of other (fixed) inputs. According to the table, the MPP declines with the third worker. An MPP of 20 for the third worker is less than an MPP of 26 for the second worker. (E) worker 7 (F) worker 8
6. Given the following production function for the mythical Tight Jeans Corporation, calculate the marginal physical product and answer three questions about marginal productivity. A) Calculate the marginal physical product. At what level of employment does: B) the law of diminishing returns become apparent? C) MPP hit zero? D) MPP become negative?
(A) LABOR INPUT: 0/1/2/3/4/5/6/7/8 OUTPUT: 0/10/36/56/68/74/76/76/74a. MPP: --/10/26/20/12/6/2/0/-2 (a) The marginal physical product is the change in output when one more worker is hired. It is calculated as the change in output divided by the change in the number of workers [= (Q2 − Q1) ÷ (L2 − L1)]. For example, when one worker is hired the marginal physical product is 10 [= (10 − 0) ÷ (1 − 0)], when a second worker is hired the marginal physical product is 26 [= (36 − 10) ÷ (2 − 1)], and so on. (B) worker 3 (b) The law of diminishing returns states that the marginal physical product (MPP) of a variable input declines as more of it is employed with a given quantity of other (fixed) inputs. According to the table, the MPP declines with the third worker. An MPP of 20 for the third worker is less than an MPP of 26 for the second worker. (C) worker 7 (D) worker 8
7. Given the following production function for the mythical Tight Jeans Corporation, calculate the marginal physical product and the value of the marginal physical product. Assume a price of $30 per pair of jeans. Note the value of the marginal physical product is the price of the product multiplied by the marginal physical product.
(A) LABOR INPUT: 0/1/2/3/4/5/6/7/8 OUTPUT: 0/10/36/56/68/74/76/76/74a. MPP: --/10/26/20/12/6/2/0/-2 VALUE OF MPP:-/300/780/600/360/180/60/0/-60 (a) The marginal physical product is the change in output when one more worker is hired. It is calculated as the change in output divided by the change in the number of workers [= (Q2 − Q1) ÷ (L2 − L1)]. For example, when one worker is hired the marginal physical product is 10 [= (10 − 0) ÷ (1 − 0)], when a second worker is hired the marginal physical product is 26 [= (36 − 10) ÷ (2 − 1)], and so on. The value of the MPP is price times the MPP (= price × MPP). For example, the MPP for the third worker is 20 and the price per pair of jeans is $30, yielding a value of $600 (= 20 × $30). The MPP for the seventh worker is zero, which yields a value of $0 (= 0 × $30).
1. In the table below, calculate the marginal physical product of each successive worker and answer questions about production. A) Calculate the marginal physical product of each successive worker. B) For which worker is marginal physical product first diminishing/zero?
(A) LABOR INPUT: 0/1/2/3/4/5/6/7/8 OUTPUT: 0/15/34/44/48/50/51/51/47 MPP: 15/19/10/4/2/1/0/-4 (a) Marginal physical product (MPP) is the change in total output associated with one additional unit of input. In our example, marginal physical product is the extra output obtained by hiring one more worker. It is calculated as the change in total output (quantity) divided by the change in the number of workers. MPP of the first worker = (total output with the first worker − total output of no workers) ÷ (one more worker) = (15 − 0) ÷ 1 = 15 MPP of the second worker = (total output with the second worker − total output of first worker) ÷ (one more worker) = (34 − 15) ÷ 1 = 19 (B) worker 3/worker 7 (b) The relative scarcity of other inputs (capital and land) constrains the marginal physical product of labor and eventually causes it to diminish. The law of diminishing returns states that the MPP of a variable input declines as more of it is employed with a given quantity of other (fixed) inputs. In this case, the MPP first diminished with worker number 3. According to the table, the MPP of worker number 7 is zero.
11. If the world's population is growing by 1 percent a year, (A) how fast does production have to increase to keep living standards constant? (B) how will living standards change if the workforce and productivitiy (marginal physical product, MPP) also increase by 1 percent each year?
(A) Living standards will remain constant if the increase in production is equal to 1% a year (a) Living standards will be maintained if the economy's production keeps up with its population growth. In this example, since population is growing at 1 percent a year, living standards will be maintained if the increase in production is also equal to 1 percent a year. • Living standards will fall if the increase in production is less than the growth in population. • Living standards will rise if the increase in production is greater than the growth in population. (B) Living standards will stay the same. (b) Marginal physical product (MPP) is the change in total output that occurs when workers are added. • If population, workforce, and MPP are all rising at the same rate, living standards would be maintained. • If the population rises faster than the workforce and MPP, then living standards will fall. • If the population rises slower than the workforce and MPP, then living standards will rise.
4. A) Complete the following table. B) What output has the lowest per-unit cost equal to marginal cost? C) What is the value of fixed costs?
(A) RATE OF OUTPUT: 0/1/2/3/4/5 TOTAL COST: 80/80/100/120/160/250 MARGINAL COST: --/10/10/20/40/90 ATC: --/90/50/40/40/50 (a) Marginal cost is the increase in total cost associated with a one-unit increase in production. It is calculated as the change in total cost divided by the change in output [= (TC2 − TC1) ÷ (Q2 − Q1)]. For example, the first unit of output has a marginal cost of $10 [= ($90 − $80) ÷ (1 − 0)], the second unit has a marginal cost of $10 [= ($100 − $90) ÷ (2 − 1)], and so on. Average total cost (ATC) is total cost divided by the quantity produced. In this case, ATC for the first unit is $90 (= $90 ÷ 1), ATC for the second unit is $50 (= $100 ÷ 2), and so on. (B) 4 units (b)ATC is at a minimum at 4 units of output and a per-unit cost of $40 (C) 80 (c) Fixed costs are the costs of production that do not change when the rate of output is altered, e.g., the cost of basic plant and equipment. Recall that total cost equals fixed costs plus variable costs. If there is no output produced (output = 0), variable cost = $0. Fixed costs are the costs that exist when output is zero—in this instance, $80.
3. A) Complete the following table. B) What output has the lowest per-unit cost equal to marginal cost? C) What is the value of fixed costs? D) Plot the marginal cost and average total cost curves on a graph.
(A) RATE OF OUTPUT: 0/1/2/3/4/5 TOTAL COST: 80/80/100/120/160/250 MARGINAL COST: --/10/10/20/40/90 ATC: --/90/50/40/40/50 (a) Marginal cost is the increase in total cost associated with a one-unit increase in production. It is calculated as the change in total cost divided by the change in output [= (TC2 − TC1) ÷ (Q2 − Q1)]. For example, the first unit of output has a marginal cost of $10 [= ($90 − $80) ÷ (1 − 0)], the second unit has a marginal cost of $10 [= ($100 − $90) ÷ (2 − 1)], and so on. Average total cost (ATC) is total cost divided by the quantity produced. In this case, ATC for the first unit is $90 (= $90 ÷ 1), ATC for the second unit is $50 (= $100 ÷ 2), and so on. (B) 4 units (b)ATC is at a minimum at 4 units of output and a per-unit cost of $40 (C) 80 (c) Fixed costs are the costs of production that do not change when the rate of output is altered, e.g., the cost of basic plant and equipment. Recall that total cost equals fixed costs plus variable costs. If there is no output produced (output = 0), variable cost = $0. Fixed costs are the costs that exist when output is zero—in this instance, $80. (d) The two curves (marginal cost and average total cost) are plotted on the graph. Examples of points on the marginal cost curve are Q = 1; MC = $10 and Q = 2; MC = $10, and so on. The average total cost curve is plotted in a similar way.
2. In the table below, compute average fixed costs and average variable costs for all rates of output and answer questions about average costs. A) Compute average fixed costs and average variable costs for all rates of output. B) At what rate of output is AFC the lowest/AVC the lowest/ATC the lowest?
(A) RATE OF OUTPUT: 0/10/15/20/30/40/50/51 FIXED COSTS: 120 AFC: --/12/8/6/4/3/2.40/2.35a. VARIABLE COSTS: 0/85/125/150/240/350/550/633 AVC: 0/8.50/8.33/7.50/8/8.75/11/12.41a. TOTAL COST: 120/205/245/270/360/470/670/753 ATC: 20.50/16.33/13.50/12/11.75/13.40/14.76 (a) Average fixed cost is fixed cost divided by total output [= fixed cost ÷ total output]. When the rate of output is 10, average fixed cost is $12 (= $120 ÷ 10 units). When the rate of output is 15, average fixed cost is $8 (= $120 ÷ 15 units), and so on. Average variable cost is variable cost divided by total output [= variable cost ÷ total output]. When the rate of output is 10, average variable cost is $8.50 (= $85 ÷ 10 units). When the rate of output is 15, average variable cost is $8.33 (= $125 ÷ 15 units), and so on. (B) 51 units/20 units/40 units (b) According to the table, average fixed cost is lowest where the rate of output is 51 units and average fixed cost is $2.35. Note that average fixed cost always falls with increased output. Average variable cost is lowest where the rate of output is 20 units and average variable cost is $7.50. Average total cost is lowest where the rate of output is 40 units and average total cost is $11.75.
