ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS Due the Week of July 14 Chapter 11 WRITE: [2] Complete the following labour demand table for a firm that is hiring labour competitively and selling its product in a competitive market. Labour Total MPP Price TR MRP 0 0 $2 $0 17 $34 1 17 $2 $34 14 $28 2 31 $2 $62 12 $24 3 43 $2 $86 10 $20 4 53 $2 $106 7 $14 5 60 $2 $120 5 $10 6 65 $2 $130 a. How many workers will the firm hire if the going wage rate is $27.95? $19.95? Explain why the firm will not hire a larger or smaller number of workers at each of these wage rates. b. Show in schedule form and graphically the labour demand curve of this firm. c. Now redetermine the firm s demand curve for labour, assuming that it is selling in an imperfectly competitive market and that, although it can sell 17 units at $2.20 per unit, it must lower product price by 5 cents in order to sell the marginal product of each successive labour unit. Compare this demand curve with that derived in question 2b. Which curve is more elastic? Explain. ANS: See table for marginal product data, total revenue data, and marginal revenue product data. (a) Two workers at $27.95 because the MRP of the first worker is $34 and the MRP of the second worker is $28, both exceeding the $27.985 wage. Four workers at $19.95 because workers 1 through 4 have MRPs exceeding the $19.95 wage. The fifth worker s MRP is only $14 so he or she will not be hired. (b) The demand schedule consists of the first and last columns of the table: page 1
Question 2-b Question 11-2b Quantity of labour demanded (plotted at the halfway points along the horizontal axis) (c) Reconstruct the table. Labour Total MPP Price TR MRP 0 0 $0.00 17 $37.40 1 17 $2.20 $37.40 14 $29.25 2 31 $2.15 $66.65 12 $23.65 3 43 $2.10 $90.30 10 $18.35 4 53 $2.05 $108.65 7 $11.35 5 60 $2.00 $120.00 5 $6.75 6 65 $1.95 $126.75 The new labour demand is less elastic. Here, MRP falls because of diminishing returns and because product price declines as output increases. A decrease in the wage rate will produce less of an increase in the quantity of labour demanded, because the output from the added labour will reduce product price and thus MRP. page 2
WRITE [3] Suppose that marginal product tripled while product price fell by one-half in Table 11-1. What would be the new MRP values in Table 11-1? What would be the net impact on the location of the factor demand curve in Figure 11-1? ANS: New MRP values (top to bottom): $21, 18, 15, 12, 9, 6, 3. The factor demand curve would shift up, with the MRP fifty percent greater for each quantity of factor demanded. Resource TP MPP Price TR MRP 0 0 $1 0 21 $21 1 21 $1 21 18 $18 2 39 $1 39 15 $15 3 54 $1 54 12 $12 4 66 $1 66 9 $9 5 75 $1 75 6 $6 6 81 $1 81 3 $3 7 84 $1 84 WRITE [5] What are the determinants of the elasticity of factor demand? What effect will each of the following have on the elasticity or the location of the demand for factor C, which is being used to produce commodity X? Where there is any uncertainty as to the outcome, specify the causes of that uncertainty. a. An increase in the demand for product X. b. An increase in the price of substitute factor D. c. An increase in the number of factors substitutable for C in producing X. d. A technological improvement in the capital equipment with which factor C is combined. e. A decline in the price of complementary factor E. f. A decline in the elasticity of demand for product X due to a decline in the competitiveness of the product market. page 3
ANS: Four factors determine elasticity: 1. the rate at which the factor s MP declines; 2. the ease of substituting other factors; 3. elasticity of product demand; 4. the ratio of the factor cost to the total cost of production. (a) Increase in demand C. (b) The price increase for D will increase the demand for C through the substitution effect, but decrease the demand for all factors including C through the output effect. The net effect is uncertain; it depends on which effect outweighs the other. (c) Increases the elasticity of demand for C. (d) Increases the demand for C. (e) Increases the demand for C through the output effect. There is no substitution effect. (f) Reduces the elasticity of demand for C. WRITE [6] Suppose the productivity of labour and capital are as shown below. The output of these factors sells in a purely competitive market for $1 per unit. Both capital and labour are hired under purely competitive conditions at $3 and $1 respectively. capital MP of capital labour MP of labour 1 24 1 11 2 21 2 9 3 18 3 8 4 15 4 7 5 9 5 6 6 6 6 4 7 3 7 1 8 1 8 0.5 a. What is the least-cost combination of labour and capital to employ in producing 80 units of output? Explain. b. What is the profit maximizing combination of labour and capital the firm should use? Explain. What is the resulting level of output? What is the economic profit? Is this the least costly way of producing the profit-maximizing output? page 4
ANS: (a) 2 capital; 4labour. labor. MP /P 7/ 1; MP /P 21/ 3 7/ 1. 2 C C 7 capital and 7 labor. MRP L / L 1 1 1 MRP C/PC 1 3/ (b) 7 capital and 7 labour. / 3. Output is 142 (= 96 from capital + 46 from labour). Economic profit is $114 (= $142 - $28) assuming there are no fixed costs. Yes, least-cost production is part of maximizing profits; the profit-maximizing rule includes the leastcost rule. WRITE [7] In each of the following four cases, MRP L and MRP C refer to the marginal revenue products of labour and capital, respectively, and P L and P C refer to their prices. Indicate in each case whether the conditions are consistent with maximum profits for the firm. If not, state which factor(s) should be used in larger amounts and which factor(s) should be used in smaller amounts. a. MRP $8; P $4; MRP $8; P $ 4 C C. b. MRP $ 10; P $ 12; MRP $ 14; P 9. C C $ c. MRP $ 6; P $ 6; MRP $12; P 12. C C $ d. MRP $ 22; P $26; MRP 16; P $19. C $ C ANS: (a) Use more of both. (b) Use less labour and more capital. (c) Maximum profits obtained. (d) Use less of both. CONSIDER: [1] What is the significance of factor pricing? Explain in detail how the factors determining factor demand differ from those underlying product demand. Explain the meaning and significance of the notion that the demand for a factor is a derived demand. Why do factor demand curves slope downward? ANS: All factors that enter into production are owned by someone, including the most important factor of all for most people, self-owned labour. The most basic significance of factor pricing is that it largely determines people s incomes. Factor pricing allocates scarce factors among alternative uses. Firms take account of the prices of factors in deciding how best to attain least-cost production. Finally, factor pricing has a great deal to do with income inequality and the debate as to what government should or should not do to lessen this inequality. It is here that the factors that determine factor demand are most different from those that determine demand for products. Demand for products is a question of income and tastes. But factor demand is more passive in the sense that it is derived from the demand for the products the factor can produce. If a factor can t be used in production of a desired product, there will not be any demand for it. Additionally, factors are often less mobile than products, so their geographic location relative to demand for the output they produce may be an important factor determining demand for factors in particular geographic areas. Factors of production are not hired or bought because their employer or buyer desires them for themselves. The demand for factors is entirely derived from what the firm believes the factors can produce. If there were no demand for output, there would be no demand for input. The demand for a factor depends, then, on how productive it is in producing output and on the price of the output. The demand for a factor is downsloping because of the diminishing marginal product of the factor page 5
(because of the law of diminishing returns) and, in imperfectly competitive markets, also because the greater the output, the lower its price. WRITE: During the 1980s Fraser Valley raspberry growers found it increasingly difficult to find people to pick their crops. Students were no longer willing to do the work and recent immigrants were finding better paid jobs. Many farmers purchased mechanical harvesting machines that cost upwards of $125,000. What impact did this have on the demand for human berry pickers? What does that imply about the relative strengths of the substitution and output effects? Currently some farmers are hiring Mexican pickers under the Seasonal Agricultural Workers Program (SAWP). What will happen to the demand for mechanical harvesters if this programme expands? ANS: Since farmers could not hire workers to manually pick raspberries it is likely that the machines substituted for labour. In this case the substitution effect likely dominated the output effect. Also, machine operators have a higher level of skill than hand pickers, and clearly their MRP was higher. Ceteris paribus that would mean they would earn higher wages. If the SAWP programme expands, it is likely that labour will be substituted for capital. This will depend in part on the wages paid to that labour. page 6