In: Economics
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 |
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.