Question

Managerial Economics and Strategy Chapter 6 Q7.3
​A Korean electronic chip manufacturer has a production function given by ​q = L^0.5K0.5.
​​a). Assume the wage rate is $45 and the cost of capital is $60. Use Excel to determine the amount of capital, K, needed to produce 20 units of output for each value of labor, L. starting from L=2 and going to 40 in increments of 1. Plot this isoquant. (Hint: The formula for that isoquant is 10 = L^0.5K^​0.5​. Squaring both sides of the quation, we obtain 100 = LK. Dividing both sides of the equation by L, we learn that K = 100/L.)
​b). Which combination of inputs minimizes the cost of producing 20 units of output? Hint L still starts from 2 to 40 in increments. Here you are just to write down the combination of L and K, but you should support your answer.

Answer 1

Solution:

Labor (L)	Capital (K)	Wage ($)	Capital cost ($)	Sqrt of Labor	Output	Sqrt of Capital	Capital for 20 output	Cost of labor	Cost of Capital	Total cost for 20 output
2	50	90	3000	1.4	20	14.1	200.0	180	600000.0	600180.0
3	33	135	2000	1.7	20	11.5	133.3	405	266666.7	267071.7
4	25	180	1500	2.0	20	10.0	100.0	720	150000.0	150720.0
5	20	225	1200	2.2	20	8.9	80.0	1125	96000.0	97125.0
6	17	270	1000	2.4	20	8.2	66.7	1620	66666.7	68286.7
7	14	315	857	2.6	20	7.6	57.1	2205	48979.6	51184.6
8	13	360	750	2.8	20	7.1	50.0	2880	37500.0	40380.0
9	11	405	667	3.0	20	6.7	44.4	3645	29629.6	33274.6
10	10	450	600	3.2	20	6.3	40.0	4500	24000.0	28500.0
11	9	495	545	3.3	20	6.0	36.4	5445	19834.7	25279.7
12	8	540	500	3.5	20	5.8	33.3	6480	16666.7	23146.7
13	8	585	462	3.6	20	5.5	30.8	7605	14201.2	21806.2
14	7	630	429	3.7	20	5.3	28.6	8820	12244.9	21064.9
15	7	675	400	3.9	20	5.2	26.7	10125	10666.7	20791.7
16	6	720	375	4.0	20	5.0	25.0	11520	9375.0	20895.0
17	6	765	353	4.1	20	4.9	23.5	13005	8304.5	21309.5
18	6	810	333	4.2	20	4.7	22.2	14580	7407.4	21987.4
19	5	855	316	4.4	20	4.6	21.1	16245	6648.2	22893.2
20	5	900	300	4.5	20	4.5	20.0	18000	6000.0	24000.0
21	5	945	286	4.6	20	4.4	19.0	19845	5442.2	25287.2
22	5	990	273	4.7	20	4.3	18.2	21780	4958.7	26738.7
23	4	1035	261	4.8	20	4.2	17.4	23805	4536.9	28341.9
24	4	1080	250	4.9	20	4.1	16.7	25920	4166.7	30086.7
25	4	1125	240	5.0	20	4.0	16.0	28125	3840.0	31965.0
26	4	1170	231	5.1	20	3.9	15.4	30420	3550.3	33970.3
27	4	1215	222	5.2	20	3.8	14.8	32805	3292.2	36097.2
28	4	1260	214	5.3	20	3.8	14.3	35280	3061.2	38341.2
29	3	1305	207	5.4	20	3.7	13.8	37845	2853.7	40698.7
30	3	1350	200	5.5	20	3.7	13.3	40500	2666.7	43166.7
31	3	1395	194	5.6	20	3.6	12.9	43245	2497.4	45742.4
32	3	1440	188	5.7	20	3.5	12.5	46080	2343.8	48423.8
33	3	1485	182	5.7	20	3.5	12.1	49005	2203.9	51208.9
34	3	1530	176	5.8	20	3.4	11.8	52020	2076.1	54096.1
35	3	1575	171	5.9	20	3.4	11.4	55125	1959.2	57084.2
36	3	1620	167	6.0	20	3.3	11.1	58320	1851.9	60171.9
37	3	1665	162	6.1	20	3.3	10.8	61605	1753.1	63358.1
38	3	1710	158	6.2	20	3.2	10.5	64980	1662.0	66642.0
39	3	1755	154	6.2	20	3.2	10.3	68445	1577.9	70022.9
40	3	1800	150	6.3	20	3.2	10.0	72000	1500.0	73500.0