Question

A Korean electronic chip manufacturer has a production function given by Q=L^(0.5)K^(0.5). Assume the Wage rate is $45 and the cost of capital is $60. Use the 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 and upload your excel sheets.

A Korean electronic chip manufacturer has a production function given by Q=L^(0.5)K^(0.5). Assume the Wage rate is $45 and the cost of capital is $60. Use the Excel to determine the cost of each these combinations of K and L. 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 just to write down the combination of L and K, but you should support your answer by your excel sheets.

Answer 1

The production function is given by Q=L^(0.5)K^(0.5). Output is 20 units. Costs are w = $45 and r = $60. This makes the production function 20 = L^(0.5)K^(0.5). or K = (20/L^0.5)^2. For 2 < L < 40, below is the data for values of capital required at each level of L. Cost function is C = 45L + 60K. For each of the combinations, the table shows the cost. For example, when L is 16, K is 25 and Q is 20. Cost is 45*16 + 60*25 = $2220

Optimum combination is L = 23 and K = 17.4

Labor	Capital	Budget
2	200.0	12090.0
3	133.3	8135.0
4	100.0	6180.0
5	80.0	5025.0
6	66.7	4270.0
7	57.1	3743.6
8	50.0	3360.0
9	44.4	3071.7
10	40.0	2850.0
11	36.4	2676.8
12	33.3	2540.0
13	30.8	2431.2
14	28.6	2344.3
15	26.7	2275.0
16	25.0	2220.0
17	23.5	2176.8
18	22.2	2143.3
19	21.1	2118.2
20	20.0	2100.0
21	19.0	2087.9
22	18.2	2080.9
23	17.4	2078.5
24	16.7	2080.0
25	16.0	2085.0
26	15.4	2093.1
27	14.8	2103.9
28	14.3	2117.1
29	13.8	2132.6
30	13.3	2150.0
31	12.9	2169.2
32	12.5	2190.0
33	12.1	2212.3
34	11.8	2235.9
35	11.4	2260.7
36	11.1	2286.7
37	10.8	2313.6
38	10.5	2341.6
39	10.3	2370.4
40	10	2400.0