Answer:
The firm should use 10 hours of labor (L) and produce 10 units of output (Q).
Explanation:
In economics, Total revenue (TR) is the multiplication of the number of units of output produced (i.e. Q) and the market price (i.e. P). Since Q = 20L - L^2 and P = $44, therefore,
TR = Q*P
= (20L - L^2)44
TR = 880 - 44L^2 ........................................... (1)
Total cost (TC) is the multiplication of the number of units of output produced (i.e. Q) and the wage rate (i.e. w). Since Q = 20L - L^2 and w = $1010, therefore,
TC = Q*w
= (20L - L^2)1010
TC = 20200 - 1010L^2 ....................................... (2)
In economics, is Profit (Pr) TR minus TC, therefore:
Pr = TR - TC
Pr = (880 - 44L^2) - (20200 - 1010L^2)
= 880 - 44L^2 - 20200 + 1010L^2
= 1010L^2 - 44L^2 - 20200 + 880
Pr = 966L^2 - 19320 ....................................... (3)
In economics, profit is maximized when equation (3) is differentiated with respect to L and equated to zero as follows:
dPr/dL = 2(966)L - 19320 = 0
1932L = 1932
0
L = 19320
/1932
L = 10
To get Q, we substitute L = 1 into Q = 2L - L^2 as follows:
Q = 2(10) - (10)^2
= 20 - 10
Q = 10
Since L = 10 and Q = 10 when the profit is maximized, the firm should use 10 hours of labor (L) and produce 10 units of output (Q).
