Question

Labor markets and wage determination

Table 1. Chocolate chip cookie output and number of workers. Cookies sell for $2.00 each.

Workers	cookie output
1	30.0
2	58.5
3	85.5
4	111.0
5	135.0
6	157.5
7	178.5
8	198.0
9	216.0
10	232.5

a) (1 point) Nick Seaman (Black Sheep Bakery in Amherst) has estimated the number of brownies produced for different numbers of workers (see table 1). Why does output increase with more workers? Why does output increase at a diminishing rate? Would output increase at a diminishing rate if there were additional ovens and workspace?

b) (1 point) Cookies sell for $2 each and each requires $0.75 in ingredients. (The Black Sheep uses quality chocolate!) Graph the demand for labor as a function of the wage using the data in table 1. What happens to the number of workers hired when wages go up? How many workers will be hired and how many cookies made at a wage of $22.50?

c) (2 points) Nick could buy a 2nd oven. He estimates that the 2nd oven would raise output for any given number of workers as indicated in table 2. When his workers form a union, they gain a wage increase from $22.50 to $24.38. What do you expect to happen to employment and output with one oven? (How many workers will be hired and how much produced at the new wage.) What would happen if Nick responds to the wage increase by buying a 2nd oven and then hiring workers at the wage $24.38? Would your answer change any if there is a limited market for chocolate chip cookies so that Nick would have to lower the price of cookies to sell more?

Workers	cookie output with 2 ovens
1	35.0
2	69.5
3	103.5
4	137.0
5	170.0
6	202.0
7	233.0
8	263.0
9	291.5
10	318.5

d) (1 point) Like many retail employers, Nick experiences high turnover among his workers which forces him to devote much time to hiring and training workers. By establishing systems for seniority promotion and pension and insurance benefits as well as higher wages, the union discourages turnover saving Nick money by making each worker more productive at higher wages. Now draw a hypothetical labor demand curve assuming higher wages are associated with higher productivity.

Answer 1

a) Output increases with increased number of workers. This is because as the variable factor labor increases, the amount of output produced by the worker also increases. The Total Product produced by the increased number of workers increases.

Output increases at a diminishing rate due to Law of Variable proportions. Initially, the fixed factor is sufficient to hold additional worker and additional raw materials to produce the output at an increasing rate. Gradually when the fixed factor, microwave oven and workspace becomes a constraint, the output increases with the increase in labors but at a diminishing rate.

At this time if the fixed factor, microwave oven and workspace also increases proportionately with the labors, the output finally increases again with increasing rate.

b) As the wage rises, there would be a reduction in the demand of labors. This is because in order to compensate for the rise in wages, the manufacturer reduces the labor force working in order to maintain the same level of cost of production.

As the Wages increase from W1 to W2, the quantity of labors hired reduces from Q1 to Q2.

Workers	Cookie Output	Total Cost	Total Revenue	Marginal Cost	Marginal Revenue
1	30	22.5 + (0.75*30) = 45	30*2 = 60
2	58.5	2*22.5 + (0.75*58.5) = 88.88	58.5*2 = 117	88.88-45 = 43.88	117-60=57
3	85.5	3*22.5 + (0.75*85.5) = 131.63	85.5*2 = 171	131.63-88.88 = 42.75	171-117=54
4	111	4*22.5 + (0.75*111) = 173.25	111*2 = 222	173.25-131.63 = 41.62	222-171=51
5	135	5*22.5 +( 0.75*135) = 213.75	135*2 = 270	213.75-173.25 = 40.5	270-222=48
6	157.5	6*22.5 + (0.75*157.5) = 253.13	157.5*2 = 315	253.13-213.75 = 39.38	315-270=45
7	178.5	7*22.5 + (0.75*178.5) = 291.36	178.5*2 = 357	291.36-253.13 = 38.23	357-315=42
8	198	8*22.5 + (0.75*198) = 328.5	198*2 = 396	328.5-291.36 = 37.14	396-357=39
9	216	9*22.5 + (0.75*216) = 364.5	216*2 = 432	364.5-328.5 = 36	432-396=36
10	232.5	10*22.5 + (0.75*232.5) = 399.38	232.5*2 = 465	399.38-364.5 = 34.88	465-432=33

At a wage of $22.50, the number of cookies made would be where MR = MC. Thus 9 workers would be hired and 216 cookies would be made.

c)

Workers	Cookie Output	Total Cost	Total Revenue	Marginal Cost	Marginal Revenue
1	35	24.38 + (0.75*35)= 50.63	35*2 = 70
2	69.5	2*24.38+ (0.75*69.5) = 100.89	69.5*2 = 139	100.89-50.63 = 50.26	139-70=69
3	103.5	3*24.38 + (0.75*103.5)= 150.77	103.5*2 = 207	150.77-100.89=49.88	207-139=68
4	137	4*24.38+ (0.75*137)= 200.27	137*2 =274	200.27-150.77=49.5	274-207=67
5	170	5*24.38+( 0.75*170) = 249.4	170*2 = 340	249.4-200.27=49.13	340-274=66
6	202	6*24.38+ (0.75*202)= 297.78	202*2 = 404	297.78-249.4=48.38	404-340=64
7	233	7*24.38+ (0.75*233)= 345.41	233*2 = 466	345.41-297.78=47.63	466-404=62
8	263	8*24.38+ (0.75*263) = 392.29	263*2 = 526	392.29-345.41=46.88	526-466=60
9	291.5	9*24.38+ (0.75*291.5)= 438.05	291.5*2 = 583	438.05-392.29=45.76	583-526=57
10	318.5	10*24.38+ (0.75*318.5)= 482.66	318.5*2 = 637	482.66-438.05=44.61	637-583=54

As the wage increases, the labors would be chucked out of the job and thus the level of unemployment increases. But at the same time, the level of output increases with increased wages as the efficiency increases. Moreover, additional oven would increase the fixed component and thus there would be increased level of output.

The answer would change as Nick reduces the price of cookies as the overall revenue earned reduces in that case.

d)