In: Economics
The short-run production function for sea kayaks is given by Q = 30L^0.5 (read as Q = 30 times L taken to the power of 0.5), where Q is the number of sea kayaks produced and L is the number of employees. Complete this table and round all answers to two decimal points:
L |
Q |
MPL |
APL |
0 |
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1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
In this space, graph the short-run production function, show labels! |
In this space, graph the marginal product of labor and average product of labor, show labels! |
The short-run production function for sea kayaks is given by Q = 30L^0.5.
And the table below has Labor (L) given as 0,1,2,3,4,5,6 and 7. So, substituiting the values of L in the short-run production function we get the output i.e. Quantity (Q).
When L = 0, Q = 30*(0)^0.5 = 0,
when L = 1, Q = 30*(1)^0.5 = 30*1 = 30,
when L = 2, Q = 30*(2)^0.5 = 30*1.414 = 42.42,
when L = 3, Q = 30*(3)^0.5 = 30*1.732 = 51.96,
when L = 4, Q = 30*(4)^0.5 = 30*2 = 60,
when L = 5, Q = 30*(5)^0.5 = 30*2.236 = 67.08,
when L = 6, Q = 30*(6)^0.5 = 30*2.449 = 73.47,
when L = 7, Q = 30*(7)^0.5 = 30*2.646 = 79.38.
Maginal Product of Labor is the change in output with one additional change in labor. It is calculated by subtracting the previous output from the present output. The Average Product of Labor is the total product of labor divided by the labor employed.
When L = 0, MPL = 0, APL = 0,
When L = 1, MPL = 30 - 0, = 30 and APL = 30/1 = 30,
When L = 2, MPL = 42.42 - 30, = 12.42 and APL = 42.42/2 = 21.21,
When L = 3, MPL = 51.96 - 42.42, = 9.54 and APL = 51.96/3 = 17.32 and so on.
The values are entered in the table given below:
L | Q | MPL | APL |
0 | 0 | 0 | 0 |
1 | 30 | 30 | 30 |
2 | 42.42 | 12.42 | 21.21 |
3 | 51.96 | 9.54 | 17.32 |
4 | 60 | 8.04 | 15 |
5 | 67.08 | 7.08 | 13.42 |
6 | 73.47 | 6.39 | 12.25 |
7 | 79.38 | 5.91 | 11.34 |
The graph the short-run production function is drawn below:
The Graph of the marginal product of labor and average product of labor is drawn below: