Dirt Diggers (DD) is a firm that excavates roadside ditches to lay drainpipe. It
ID: 1193149 • Letter: D
Question
Dirt Diggers (DD) is a firm that excavates roadside ditches to lay drainpipe. Its output follows the production function: Q = 10L 0.1L 2 , where L denotes labor hours and Q the length of the ditch in meters. The marginal product of labor is MPL = 10 0.2L The firm hires labor at a wage of $12 per hour. A) Should DD accept an offer to excavate 250 meters for a price of $500? Explain. B) Suppose DD from question 1 is offered as much or as little excavation work as it desires at a price of $2.00 per meter. Should it accept this offer and what will it produce if it does?
Explanation / Answer
a )
Q= 10L-.1L^2
Putting Q= 250
Equation will be 250= 10L-.1 L^2
.1L^2-10L +250 = 0
Solving for L ; L=50
Which means for producing 250 metres 50 labour hours is required.
For 50 labour hours firm will have to pay = 50* 12 = 600 to labours
As the cost 600 > price (500); firm shouldn't accept an offer.
b ) If the firm employs 39 labors then it can produce 234 meters.
For 39 labours it'll have to pay = 39*12 = 468
And for 234 meters it can charge 2 * 234 = 468. So for anything less than 39 labour or less than 234 metres should be accpeted as it'll provide some profit to DD.
Labour MPL Total output 1 9.8 9.8 2 9.6 19.4 3 9.4 28.8 4 9.2 38 5 9 47 6 8.8 55.8 7 8.6 64.4 8 8.4 72.8 9 8.2 81 10 8 89 11 7.8 96.8 12 7.6 104.4 13 7.4 111.8 14 7.2 119 15 7 126 16 6.8 132.8 17 6.6 139.4 18 6.4 145.8 19 6.2 152 20 6 158 21 5.8 163.8 22 5.6 169.4 23 5.4 174.8 24 5.2 180 25 5 185 26 4.8 189.8 27 4.6 194.4 28 4.4 198.8 29 4.2 203 30 4 207 31 3.8 210.8 32 3.6 214.4 33 3.4 217.8 34 3.2 221 35 3 224 36 2.8 226.8 37 2.6 229.4 38 2.4 231.8 39 2.2 234 40 2 236 41 1.8 237.8 42 1.6 239.4 43 1.4 240.8 44 1.2 242 45 1 243 46 0.8 243.8 47 0.6 244.4 48 0.4 244.8 49 0.2 245 245 490Related Questions
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