Managerial Economics Chapter 5 and 6 Homework
Chapter 5 Question 6 Page 218
Q = Dresses per week
L= Number of labor hours per week
Q = L –L2/800
MCL=$20
P= $40= therefore MR=$40
Part A:
A firm maximizes profit when it equates MRPL = (MR) *(MPL) = MCL
MPL= dQ/dL =1 – L/400
Therefore (40)*(1-L/400) = 20. The solution is L = 200.
In turn, Q = 200 – (2002/800). The solution is Q = 150.
The firms profit is= PQ – (MC)L= ($40) (150) – ($20) (200) = $2,000
Part B Price increase to $50:
Q = Dresses per week
L= Number of labor hours per week
Q = L –L2/800
MCL=$20
P= $50
A firm maximizes profit when it equates MRPL = (MR) *(MPL) = MCL
MPL= dQ/dL =1 – L/400
Therefore (50)*(1-L/400) = 20. The solution is L = 240.
In turn, Q = 240 – (2402/800). The solution is Q = 168.
The firms profit is ($40) (168) – ($20) (240) = $1,920
Optimal output of the firm would increase from 150 to 168, and labor would increase from 200 to 240, resulting in a decrease in profit to $1,920.
Part B inflation in labor and output price:
Assuming a 10% increase IN LABOR COST AND OUTPUT PRICE…
Q = Dresses per week
L= Number of labor hours per week
Q = L –L2/800
MCL=$20.20 (20*.10)
P= $40.40 ($40*.10)
A firm maximizes profit when it equates MRPL = (MR) *(MPL) = MCL
MPL= dQ/dL =1 – L/400
Therefore (40.40)*(1-L/400) = 20.20. The solution is L = 200.
In turn, Q = 200 – (2002/800). The solution is Q = 150.
The firms profit is ($40.40) (150) – ($20.20) (200) = $2,020
Optimal output of the firm would remain the same at 150, and labor would remain the same at 200, however, there would be an increase in profit to $2,020 to correspond to the percentage increase in output price and labor cost (in this example 10%).
Part C 25% increase in MPL:
The marginal cost of labor would increase by the same percentage amount as price (25%), therefore the Marginal Cost of labor would increase from 20 to 25.
Therefore 50 – L/8 =25 and L=200
Output and hours of labor remain unchanged due to the fact that price and cost of
Q = Dresses per week
L= Number of labor hours per week
Q = L –L2/800
MCL=$20
P= $40= therefore MR=$40
Part A:
A firm maximizes profit when it equates MRPL = (MR) *(MPL) = MCL
MPL= dQ/dL =1 – L/400
Therefore (40)*(1-L/400) = 20. The solution is L = 200.
In turn, Q = 200 – (2002/800). The solution is Q = 150.
The firms profit is= PQ – (MC)L= ($40) (150) – ($20) (200) = $2,000
Part B Price increase to $50:
Q = Dresses per week
L= Number of labor hours per week
Q = L –L2/800
MCL=$20
P= $50
A firm maximizes profit when it equates MRPL = (MR) *(MPL) = MCL
MPL= dQ/dL =1 – L/400
Therefore (50)*(1-L/400) = 20. The solution is L = 240.
In turn, Q = 240 – (2402/800). The solution is Q = 168.
The firms profit is ($40) (168) – ($20) (240) = $1,920
Optimal output of the firm would increase from 150 to 168, and labor would increase from 200 to 240, resulting in a decrease in profit to $1,920.
Part B inflation in labor and output price:
Assuming a 10% increase IN LABOR COST AND OUTPUT PRICE…
Q = Dresses per week
L= Number of labor hours per week
Q = L –L2/800
MCL=$20.20 (20*.10)
P= $40.40 ($40*.10)
A firm maximizes profit when it equates MRPL = (MR) *(MPL) = MCL
MPL= dQ/dL =1 – L/400
Therefore (40.40)*(1-L/400) = 20.20. The solution is L = 200.
In turn, Q = 200 – (2002/800). The solution is Q = 150.
The firms profit is ($40.40) (150) – ($20.20) (200) = $2,020
Optimal output of the firm would remain the same at 150, and labor would remain the same at 200, however, there would be an increase in profit to $2,020 to correspond to the percentage increase in output price and labor cost (in this example 10%).
Part C 25% increase in MPL:
The marginal cost of labor would increase by the same percentage amount as price (25%), therefore the Marginal Cost of labor would increase from 20 to 25.
Therefore 50 – L/8 =25 and L=200
Output and hours of labor remain unchanged due to the fact that price and cost of