Question

Table 1. Chocolate chip cookie output and number of workers. Cookies sell for $2.50 each. Ingredients (butter, eggs, flour, nuts, sugar, vanilla how many workers will be hired and how many cookies made if the wage falls to $14) cost $0.50 for each cookie.

Workers	output( brownies)
1	10
2	34
3	57
4	78
5	97
6	114
7	129
8	142
9	152
10	159
11	163
12	164
13	164
14	163
15	161
16	158
17	154
18	149
19	143
20	136

(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 $2.50 each and each requires $0.50 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 $26? How many workers will be hired and how many cookies made if the wage falls to $14?

(c) (1 point) Nick could buy a 2^nd oven. He estimates that the 2^nd oven would raise output for any given number of workers as indicated in table 2. How many workers will be hired and how many cookies produced with two ovens at a wage of $26? 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?

Table 2. Workers and output, two ovens

Workers	output
1	40
2	79
3	117
4	154
5	190
6	224
7	256
8	286
9	314
10	340
11	364
12	386
13	406
14	424
15	439
16	452
17	462
18	469
19	473
20	474

1. (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. He finds that paying higher wages discourages turnover saving 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.
2. (e) (1 point) If higher wages raise productivity, does supply and demand determine wages?

Answer 1

(a)

As workers increase the output increase. (Total Product is increasing)

While, the rate of growth is not the same, it increases then decreases. (Marginal Product first increases then decreases)

This means, there is diminishing marginal productivity of labor. Why? Because a limited Ovens will need limited workers to work. Initial workers will be highly productive, taking up segments of the works. But, later on these workers will not have sufficient ovens to work on. Also, workspace is limited.

What if workspace and ovens increase as well, along with increase in workers?

Well, thats the best, then marginal product will keep on rising. But, the problem is Capital is not variable in Short Run. Workers are variable in Short Run, but Capital is not. So, in Long run, if workers and capital both are increasing the marginal product will also rise.

(b)

Contribution per brownie		2
				If wage is 26		If wage is 14
	Workers	output( brownies)	Output per worker	Total Contribution	Worker cost	Profit	Worker cost	Profit
1	10	10.00	20	26	-6	14	6
2	34	17.00	68	52	16	28	40
3	57	19.00	114	78	36	42	72
4	78	19.50	156	104	52	56	100
5	97	19.40	194	130	64	70	124
6	114	19.00	228	156	72	84	144
7	129	18.43	258	182	76	98	160
8	142	17.75	284	208	76	112	172
9	152	16.89	304	234	70	126	178
10	159	15.90	318	260	58	140	178
11	163	14.82	326	286	40	154	172
12	164	13.67	328	312	16	168	160
13	164	12.62	328	338	-10	182	146
14	163	11.64	326	364	-38	196	130
15	161	10.73	322	390	-68	210	112
16	158	9.88	316	416	-100	224	92
17	154	9.06	308	442	-134	238	70
18	149	8.28	298	468	-170	252	46
19	143	7.53	286	494	-208	266	20
20	136	6.80	272	520	-248	280	-8

As per the above table, 7 workers at 26$, 129 brownies

9 workers at 14$, 152 brownies

(c)

Workers	output	Output per worker	Total Contribution	Worker cost	Profit
1	40	40.00	80	26	54
2	79	39.50	158	52	106
3	117	39.00	234	78	156
4	154	38.50	308	104	204
5	190	38.00	380	130	250
6	224	37.33	448	156	292
7	256	36.57	512	182	330
8	286	35.75	572	208	364
9	314	34.89	628	234	394
10	340	34.00	680	260	420
11	364	33.09	728	286	442
12	386	32.17	772	312	460
13	406	31.23	812	338	474
14	424	30.29	848	364	484
15	439	29.27	878	390	488
16	452	28.25	904	416	488
17	462	27.18	924	442	482
18	469	26.06	938	468	470
19	473	24.89	946	494	452
20	474	23.70	948	520	428

As per above table

15 workers at 26$, 439 brownies output.

Yes, answer will be different if selling price reduces.

(d) Higher wages increase productivity. So higher wages leads to higher output. Higher output for higher wages is acceptable, since the per worker output is not bad.

(e) Supply and demand, determine prices. And these prices along with costs will determine the profits. For maximising profits, the wages has to be balanced somewhere in between. Not too low wages (high turnover) not too high wages (high loss).