Question

In: Economics

Cost of Production in the Short-run. SHOW FORMULA IN EXCEL Price of Labor (L) is PHP...

Cost of Production in the Short-run. SHOW FORMULA IN EXCEL

Price of Labor (L) is PHP 100 while Price of Capital (K) is PhP 50. What is the best cost-minimizing combination of K and L?

Price of Capital (K) Price of Labor (L) TP aka Q Total Fixed Cost Total Variable Cost Total Cost Ave Fixed Cost Ave Variable Cost Ave Total Cost Marginal Cost
10 0 0
10 1 14
10 2 35
10 3 62
10 4 91
10 5 121
10 6 150
10 7 175
10 8 197
10 9 212
10 10 217

Solutions

Expert Solution

Solution:

With quantity of capital employed fixed at 10, fixed cost is price of capital*quantity of capital = 50*10 = 500. Similarly, total variable cost can be found using the variable input.

Total cost = total fixed cost + total variable cost

Average = total/quantity, so we can fill in the table as follows:

Capital, K Labor, L Q TFC TVC TC AFC AVC ATC
10 0 0 500 100*0 = 0 500 + 0 = 500 - - -
10 1 14 500 100*1 = 100 500 + 100 = 600 500/14 = 35.71 100/14 = 7.14 600/14 = 42.86
10 2 35 500 100*2 = 200 500 + 200 = 700 500/35 = 14.29 200/35 = 5.71 700/35 = 20
10 3 62 500 100*3 = 300 500 + 300 = 800 500/62 = 8.06 300/62 = 4.84 800/62 = 12.9
10 4 91 500 100*4 = 400 500 + 400 = 900 500/91 = 5.49 400/91 = 4.4 900/91 = 9.89
10 5 121 500 100*5 = 500 500 + 500 = 1000 500/121 = 4.13 500/121 = 4.13 1000/121 = 8.26
10 6 150 500 100*6 = 600 500 + 600 = 1100 500/150 = 3.33 600/150 = 4 1100/150 = 7.33
10 7 175 500 100*7 = 700 500 + 700 = 1200 500/175 = 2.86 700/175 = 4 1200/175 = 6.86
10 8 197 500 100*8 = 800 500 + 800 = 1300 500/197 = 2.54 800/197 = 4.06 1300/197 = 6.6
10 9 212 500 100*9 = 900 500 + 900 = 1400 500/212 = 2.36 900/212 = 4.25 1400/212 = 6.6
10 10 217 500 100*10 = 1000 500 + 1000 = 1500 500/217 = 2.3 1000/217 = 4.61 1500/217 = 6.91

Minimum average variable cost occurs at input combination of 10 units of capital and 7 units of labor, so this is the required input combination.


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