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The nation of Ectenia has 20 competitive apple orchards, which sell apples at the world price of $2. The following equations describe the production function and the marginal product of labor in each orchard:

Q = 100L L2.

MPL = 100 2L

where Q is the number of apples produced in a day, L is the number of workers, and MPL is the marginal product of labor.?

a) What is each orchard's labor demand as a ?function of the daily wage W? What is the ?market's labor demand?

b) Ectenia has 200 workers who supply their ?labor inelastically. Solve for the wage W. How many workers does each orchard hire? How much profit does each orchard owner make?

c) Calculate what happens to the income of workers and orchard owners if the world price of apples doubles to $4.

d) Now suppose the price of apples is back at $2, but a hurricane destroys half the orchards. Calculate how the hurricane affects the income of each worker and of each remaining orchard owner. What happens to the income of Ectenia as a whole?

Respuesta :

ogbe2k3

Answer:

(a)The market labor is =1000 -5 W (b) The profit is $200 (c) If the world price of apples doubles to $4 it becomes, wage is $320 and the profit is $400 (d) The income as a whole before the hurricane is $3600 and income as a whole after the hurricane is $40,000

Explanation:

Solution

Given that:

Production function Q = 100 L-L²

Marginal product of labor = MPl = 100 -2L

(a) Calculate Value of Marginal Product of Labor:

VMPl =P (MPl)

=P (100 - 2L)

Then

We substitute  world price is $2

Thus

VMPl = P (100 -2L)

=2 (100 -2L)

= 200 - 4L

Now

The daily wages are equal to the value of marginal product of labor

Thus

W =200 -4L

-4L = W - 200

4L =200 - W

L = 200- W/4

Hence the market demand for labor in Ectenia is given as follows:

L = 200- W/4 * 20

=(200 - W) *5

= 1000 -5 W

(b) Calculate the wage (W), Total workers and Total profit:

Now

The wage is given below:

200 = 1000 - 5 W

- 5W = 200 - 1000

W =-800/ 5

=$160

Thus

Ectenia supplied 200 labors, the number of worker required is given below:

Number of workers = 200/20

= 10 workers

So

We calculate the profit:

Profit = Total Revenue - Total cost

= (P *Q) - (L*W)

= 2(100 L- L²) -( L*160)

=2 (100 * 10 - (10)² - (10 * 160)

=1800 -1600

=$200

The profit is $200

(c) Here, the price doubles, so the VMPl must be raised.Thus the wage is $320. the profit is $400

VMPl = 2* (200 -4 L)

=400 - 8 L

(d) Now

The price of apples is back to $2. but hurricane destroys half the orchards.

Thus the market demand for labor comes down to half relative before.

Thus

The market demand for labor in Ectenia is given below:

L = 1000 - 5W /2

= 500 -2.5 W

Thus

the average is

200 = 500 - 2.5 W

2.5W =500 -200

W =300/2.5

=$120

The wages of labor after the hurricane is $120

Now,

Calculate the profit after hurricane:

profit = Total Revenue - Total cost

= 2(100 L - L²) - (120 * L)

= 200 L - 2L² - 120 L

= 80L -2L² -120 L

=80L - 2L²

Which is

80 * 20 - 2 * 20²

= 1600 - 800

= 800

The profit of the firm after hurricane is $800

Now,

The income of Ectenia as a whole before the hurricane is given below:

The income (Total) = Total profit  + total wages

= 20 *200 + 200 * 160

= 4000 + 3200

= $3600

The income as a whole before the hurricane is $3600

Now,

income as a whole after the hurricane is given below:

The Income (Total) = Total profit  + total wages

=20 *800 + 200 * 120

= 16000+ 24000

=$40,000

income as a whole after the hurricane is $40,000

abiolataiwo2015

Based on the information given the orchard's labor demand as a function of the daily wage W and the market's labor demand are:

Given:

Production function Q = 100 L-L²

Marginal product of labor = MPl = 100 -2L

a. Marginal Product of Labor:

Wages (W)=VPML

Wages (W)=P×(MPl)

Wages (W)=2(100 - 2L)

Wages (W)=200-4L

Let re-write the wages function so as obtain the Individual labor curve

W =200 -4L

L=50-0.25W

Market demand labor curve

L=20(50-0.25W)

L=1000-5W

Market wages

L=1000-5W

W=200-0.2L

b. Wage (W), Total workers and Total profit

Equilibrium wages

L=1000-5W

200=1000-5W

5W =800

W =800/ 5

W=$160

Since there are are 200 workers and 20 orchards in the competitive market which means that orchard will hire 10 workers.

Total workers = 200/20

Total workers = 10 worker

Cost incurred by each orchard on the number of worker employed

C=L×W

C=10×160

C=1,600

Output produced by each orchard

Q=100L--L²

Q=100(10)-(10)²

Q=900

Thus,  each orchard will produce 900 apples.

Revenue earned by each orchard

Total revenue=P×Q

Total revenue=2×900

Total revenue=1,800

Profit earned by each orchard

Profit=Total revenue-Cost

Profit=$1800-$1,600

Profit=$200

 

c. Income

VMPl = 2×(200 -4 L)

VMPl =400 - 8 L

d. Hurricane effects on each workers

The market demand for labor

L = 1000 - 5W /2

L= 500 -2.5 W

Average

200 = 500 - 2.5 W

2.5W =500 -200

W =300/2.5

W=$120

The hurricane effect is $120.

The profit after hurricane

Profit = Total Revenue - Cost

Profit= 2(100 L - L²) - (120 ×L)

Profit= 200 L - 2L² - 120 L

Profit= 80L -2L² -120 L

Profit=80L - 2L²

Hence:

Profit=80× 20 - 2 × 20²

Profit= 1600 - 800

Profit= 800

The profit after hurricane is $800.

Income of Ectenia  

Income = Total profit  +  Wages

Income= 20×200 + 200∈160

Income= 4000 + 3200

Income= $3,600

The income  before the hurricane is $3,600

Income after the hurricane

Income = Total profit  +  Wages

Income=20 ×800 + 200× 120

Income= 16000+ 24000

Income=$40,000

The income after the hurricane is $40,000.

Learn more here:https://brainly.com/question/24373602

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