Solved Problem in Economics
3- The owner of a car wash is trying to decide on the number of people to employ based on the following short production function: Q = 6 L – 0.5 L² Where Q = No. of car washes per hour L = No. of workers
a- Generate a schedule showing TP,AP,MP., then graph it.
L | TPL | MPL | APL | 0 | 0 | 0 | - | 1 | 5.5 | 5.5 | 5.5 | 2 | 10 | 4.5 | 5 | 3 | 13.5 | 3.5 | 4.5 | 4 | 16 | 2.5 | 4 | 5 | 17.5 | 1.5 | 3.5 | 6 | 18 | 0.5 | 3 | 7 | 17.5 | -0.5 | 2.5 | 8 | 16 | -1.5 | 2 | 9 | 13.5 | -2.5 | 1.5 | 10 | 10 | -3.5 | 1 | 11 | 5.5 | -4.5 | 0.5 |
b- Suppose the price for a basic car wash (no under coating ,no wax treatments etc.) in his area of business is LE 5. How many people should he hire if he pays each worker LE 6 / he.? L | TP | MP | AP | TRP | MRP | TLC | MLC | TRP-TLC | MRP-MLC | 0 | 0 | | | 0 | | 0 | | 0 | 0 | 1 | 5.5 | 5.5 | 5.5 | 27.5 | 27.5 | 6 | 6 | 21.5 | 21.5 | 2 | 10 | 4.5 | 5 | 50 | 22.5 | 12 | 6 | 38 | 16.5 | 3 | 13.5 | 3.5 | 4.5 | 67.5 | 17.5 | 18 | 6 | 49.5 | 11.5 | 4 | 16 | 2.5 | 4 | 80 | 12.5 | 24 | 6 | 56 | 6.5 | 5 | 17.5 | 1.5 | 3.5 | 87.5 | 7.5 | 30 | 6 | 57.5 | 1.5 | 6 | 18 | 0.5 | 3 | 90 | 2.5 | 36 | 6 | 54 | -3.5 | 7 | 17.5 | -0.5 | 2.5 | 87.5 | -2.5 | 42 | 6 | 45.5 | -8.5 | 8 | 16 | -1.5 | 2 | 80 | -7.5 | 48 | 6 | 32 | -13.5 | 9 | 13.5 | -2.5 | 1.5 | 67.5 | -12.5 | 54 | 6 | 13.5 | -18.5 | 10 | 10 | -3.5 | 1 | 50 | -17.5 | 60 | 6 | -10 | -23.5 | 11 | 5.5 | -4.5 | 0.5 | 27.5 | -22.5 | 66 | 6 | -38.5 | -28.5 | 12 | 0 | -5.5 | 0 | 0 | -27.5 | 72 | 6 | -72 | -33.5 |
* If the price of labor equals 6LE / h , the firm should hire5 workers to reach its maximum profitability of 57,5LE . * Beyond that point the firm would pay more in additional labor cost than it would receive in additional revenue. C- Suppose he consider hiring students on a part time basis for LE 4 \ hr. . Do you think he should hire more students at this lower rate ? Explain.
a- Generate a schedule showing TP,AP,MP., then graph it.
L | TPL | MPL | APL | 0 | 0 | 0 | - | 1 | 5.5 | 5.5 | 5.5 | 2 | 10 | 4.5 | 5 | 3 | 13.5 | 3.5 | 4.5 | 4 | 16 | 2.5 | 4 | 5 | 17.5 | 1.5 | 3.5 | 6 | 18 | 0.5 | 3 | 7 | 17.5 | -0.5 | 2.5 | 8 | 16 | -1.5 | 2 | 9 | 13.5 | -2.5 | 1.5 | 10 | 10 | -3.5 | 1 | 11 | 5.5 | -4.5 | 0.5 |
b- Suppose the price for a basic car wash (no under coating ,no wax treatments etc.) in his area of business is LE 5. How many people should he hire if he pays each worker LE 6 / he.? L | TP | MP | AP | TRP | MRP | TLC | MLC | TRP-TLC | MRP-MLC | 0 | 0 | | | 0 | | 0 | | 0 | 0 | 1 | 5.5 | 5.5 | 5.5 | 27.5 | 27.5 | 6 | 6 | 21.5 | 21.5 | 2 | 10 | 4.5 | 5 | 50 | 22.5 | 12 | 6 | 38 | 16.5 | 3 | 13.5 | 3.5 | 4.5 | 67.5 | 17.5 | 18 | 6 | 49.5 | 11.5 | 4 | 16 | 2.5 | 4 | 80 | 12.5 | 24 | 6 | 56 | 6.5 | 5 | 17.5 | 1.5 | 3.5 | 87.5 | 7.5 | 30 | 6 | 57.5 | 1.5 | 6 | 18 | 0.5 | 3 | 90 | 2.5 | 36 | 6 | 54 | -3.5 | 7 | 17.5 | -0.5 | 2.5 | 87.5 | -2.5 | 42 | 6 | 45.5 | -8.5 | 8 | 16 | -1.5 | 2 | 80 | -7.5 | 48 | 6 | 32 | -13.5 | 9 | 13.5 | -2.5 | 1.5 | 67.5 | -12.5 | 54 | 6 | 13.5 | -18.5 | 10 | 10 | -3.5 | 1 | 50 | -17.5 | 60 | 6 | -10 | -23.5 | 11 | 5.5 | -4.5 | 0.5 | 27.5 | -22.5 | 66 | 6 | -38.5 | -28.5 | 12 | 0 | -5.5 | 0 | 0 | -27.5 | 72 | 6 | -72 | -33.5 |
* If the price of labor equals 6LE / h , the firm should hire5 workers to reach its maximum profitability of 57,5LE . * Beyond that point the firm would pay more in additional labor cost than it would receive in additional revenue. C- Suppose he consider hiring students on a part time basis for LE 4 \ hr. . Do you think he should hire more students at this lower rate ? Explain.