The nation of Ectenia has 20 competitive apple orchards, all...

The nation of Ectenia has 20 competitive apple orchards, all of which sell apples at the world price of \$2 per apple. The following equations describe the production function and the marginal product of labor in each orchard: $$Q = 100L 2 - L^2$$ $$MPL = 100 - 2L,$$ 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 doubles to \$4 per apple. d. Now suppose the price is back at \$2 per apple, 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?

The nation of Ectenia has 20 competitive apple orchards, all of which sell apples at the world price of \$2 per apple. The following equations describe the production function and the marginal product of labor in each orchard: $$Q = 100L 2 - L^2$$ $$MPL = 100 - 2L,$$ 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 doubles to \$4 per apple.
d. Now suppose the price is back at \$2 per apple, 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?

Transcript

00:01 Okay, question five is saying that the nation of echinia has 20 competitive apple orifics.

00:10 So there are 20 firms in total.

00:16 And each apple sells at $2.

00:21 All right.

00:24 And we have the following production function, which is q equals to 100 times.

00:35 L minus l square.

00:40 So the marginal product of labor is 100 minus 2 l.

00:55 So q is the number of apples they produce in a day when they use this l number of labors.

01:03 Okay, so a, what is each market labor demand as a function of the daily wage.

01:11 And what is the market's labor demand? so we know that if we have this mpl, this marginal product of labor times two, which is the price of the product, which is the price of the apple in this example, is the value of marginal product of labor, which is two times this number.

01:42 So it becomes 200 minus 4l.

01:50 So in equilibrium, this value is equal to wage.

01:58 Okay, so the answer for question a is just this.

02:01 So wage equals to 200 minus 4l.

02:07 And what is the market's labor demand? so the markets, so if we rearrange this equation, we get that l equals to 200 minus wage divided by four.

02:32 So this is the labor demand for one firm.

02:36 But now we know that there are 20 firms.

02:39 So the total labor demand will be 20 times l.

02:45 So total labor demand is big l equals to 20 times this number.

02:53 So it is going to be 1 ,000 minus 5 times wage.

03:06 So if we look at the graph, so if we try to draw this equation here, so it's a function of wage and labor.

03:23 So when a wage is 200, this firm is willing to hire zero labor, right? and when the wage is zero, this firm is willing to hire 50 laborers.

03:37 Okay, so this is the labor demand curve for one firm.

03:42 But now we have 20 firms, right? so to draw this big l here, we just have to sum up all this small labor.

03:53 So we see that, okay, if there are two firms, this x -axis becomes 100, right? because we sum the demand up like horizontally.

04:07 So three firms goes to 150.

04:10 So if we sum like 20 firms, this demand curve is going to be something.

04:15 Like this which is like super far away and this point is a thousand why is it a thousand because each firm is willing to hire 50 laborers when the wage is zero right so if all 20 firms do the same thing they're all in total they will hire thousand laborers so this blue line here is the demand curve or the total market which is also what we have here, this equation.

04:49 Okay, so question b is saying that if this country has 200 workers who supply their labor in elasticity, so what we the blue line here is the labor demand curve.

05:03 So now the question told us that, okay, now the labor supply curve is, i think i should redraw a graph.

05:12 Okay.

05:16 So now we know that we have this old labor demand curve, which looks something like this is w.

05:27 This is l.

05:29 I just say that this is 200.

05:32 When a wage is 200, people will, we demand zero labor.

05:40 And when a wage is zero, we demand a thousand.

05:44 So i'm drawing the blue line right here, but in a different scale.

05:50 Okay, so this is the labor demand right here.

05:55 And now question b tells us that we have an inelastic supply of 200 labors.

06:03 So it means that the supply curve is vertical.

06:07 So yes.

06:11 So given this information, we can solve the equilibrium wage, which is the point right here.

06:17 So we just have that this demand curve looks something like this.

06:26 L equals to, so l demand equals to a thousand minus five times which it has to equal to labor supply which is two equal to labor supply which is two 200 in this case...

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