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Answer #1

We have the following information

Production function: q(L) = 10L1/2

 Labor (L) Output Average Product Marginal Product 1 10.0 10.0 -- 2 14.1 7.1 4.1 3 17.3 5.8 3.2 4 20.0 5.0 2.7 5 22.4 4.5 2.4 6 24.5 4.1 2.1 7 26.5 3.8 2.0 8 28.3 3.5 1.8 9 30.0 3.3 1.7

Average product (AP) of labor is total output divided by the total quantity of labor. Marginal product (MP) of labor is change in total output as the labor unit is increased by one.

It is given that the fixed cost is \$100. Moreover, the price of labor is \$20 which can be taken as the variable cost as well as the wage rate

 Labor (L) Fixed Cost (\$) Variable Cost (\$) Total Cost (\$) Marginal Cost (\$) 1 100 20 120 -- 2 100 40 140 20 3 100 60 160 20 4 100 80 180 20 5 100 100 200 20 6 100 120 220 20 7 100 140 240 20 8 100 160 260 20 9 100 180 280 20

The equilibrium level of labor can be attained by equating the wage rate (\$20) with the value of marginal product (VMP) of labor which marginal product of labor multiplied by the price of the output (\$9)

 Labor (L) Output Average Product Marginal Product Fixed Cost (\$) Variable Cost (\$) Total Cost (\$) Marginal Cost (\$)/Wage Rate Price (\$) VMP 1 10.0 10.0 -- 100 20 120 -- 9 -- 2 14.1 7.1 4.1 100 40 140 20 9 37 3 17.3 5.8 3.2 100 60 160 20 9 29 4 20.0 5.0 2.7 100 80 180 20 9 24 5 22.4 4.5 2.4 100 100 200 20 9 21 6 24.5 4.1 2.1 100 120 220 20 9 19 7 26.5 3.8 2.0 100 140 240 20 9 18 8 28.3 3.5 1.8 100 160 260 20 9 16 9 30.0 3.3 1.7 100 180 280 20 9 15

From the table above one can see that the equilibrium level of labor is 5 units.

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