Question

Please, I need workings, I was confused about it, tries may time l did not get the answers.

thanks for your help

Amy's Hair Dressing hires hairdressers in a competitive market. The cost for a haircut, other than the labour cost, is €4. The daily number of haircuts varies with the number of workers hired, as shown in the table below:

No of workers haircut per day

0 0

1 16

2 36

3 54

4 70

5 84

6 96

1. The marginal product of the 5th worker is

2. If the price of a haircut is €10, what is the value marginal product for the 3rd worker?

3. If the price of a haircut is €10, and the competitive market wage for a hairdresser is €90 per day, how many workers should Amy hire?

4. If the price of a haircut is €10, and the competitive market wage for a hairdresser is €90 per day, how many haircuts will Amy produce each day?

5- If the price of a haircut is €12, the value marginal product for the second worker is

6. If the price of a haircut is €12, and the competitive market wage for a hairdresser is €100 per day, how many haircuts will Amy produce each day?

7. If the price of a haircut increased from €10 to €15, and the competitive market wage for a hairdresser also increased from €90 to €100 per day, how many haircuts will Amy produce each day?

8. If the price of a haircut increased from €10 to €15, and the competitive market wage for a hairdresser also decreased from €90 to €80 per day, how many workers should Amy hire?

Answer 1

1.

Marginal product of labor is the increase in the output by one additional unit of labor keeping all other factors constant. It is given by

$MP_L = \frac{\mathrm{d} Q}{\mathrm{d} L} = \frac{ \Delta Q}{\Delta L}$

Thus, marginal product of the 5th worker is:

$MP_L = \frac{ \Delta Q}{\Delta L} = \frac{84-70}{5-4} = 14$

2.

Price = 10

Marginal product of the labor for the 3rd worker-

$MP_L = \frac{ \Delta Q}{\Delta L} = \frac{54-36}{3-2} = 18$

Thus value of the marginal product for the third labor

$V = pMP_L = 10*18 = 180$

3.

Price P = 10

Cost c = 4

Competitive wage per day w = 90

Revenue per haircut R= P - c = 10 - 4= 6

Workers will be hired till the point where revenue of marginal product of labor = cost of labor

i.e. for optimal hiring-

$RMP_L = w \Rightarrow 6MP_L = 90 \Rightarrow MP_L = 15$

No. of workers hired should be such that $MP_L \leq 15$

Closest would be L = 5 where MPL = 84-70/(5-4) = 14

4.

From the table it can be seen that at L = 5, no. of haircuts produced = 84.