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Smiling Cow Dairy can sell all the milk it wants …

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Problem 3 Hard Difficulty

Suppose that labor is the only input used by a perfectly competitive firm. The firm's production function is as follows:

a. Calculate the marginal product for each additional worker.
b. Each unit of output sells for \$10. Calculate the value of the marginal product of each worker.
c. Compute the demand schedule showing the number of workers hired for all wages from zero to \$100 a day.
d. Graph the firm's demand curve.
e. What happens to this demand curve if the price of output rises from \$10 to \$12 per unit?

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Principles of Economics

Chapter 18

The Markets for the Factors of Production

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in question three. We have this following chart off the firm's production function, so because they calculated the margin product for each additional worker. So this is the most basic question. So we just have to see that away from 0 to 1. So the days of labor here means that each day they hire one more labor. So from day zero today one there hire this one more labor which produced seven units of output. So the marginal product for this first this first labour is seven. So from they want today to this second labour produced six extra unit his 30 minus 76 Okay, so the third, the third labor produced 19 minus 13 which is also six. And then the fourth labor produced 25 minus 19 which is also six. And then the fifth Labour produce green extra units and then six flavor produced only one unit on What about hiring the seven? Um, the seven labour would use nothing. So maybe all the resource is are already used up. That's why the this the last Labour does not contribute anything. Okay, Could you be each unit of outward sells for $10 to calculate a value off the marginal product off each worker. So all the blue numbers here are the marginal product. So what about the value ofthe marginal project? The value off marginal product ofthe labor isjust that the price out the quantity they produced times this marginal product ofthe labor. Okay, so, uh, here. So I was just time times 10. So the market value of margin Rallo labor is just 70 for priests flavour and then 60 for the second labour and also 60. So all this column on the left hand side, times by tens. Okay, So 70 60 60 here also 16 and then 30 and then 10. And then the value ofthe the last worker is zero because he produces nothing. Okay, See, computer, The man schedule shown the number off workers hired for all wages from 0 to 100 a day. D is graft difference? Timid occur. So I would just do both at the same time so that the men crew for labor iss, something like this and the X axis is the wage which is also equal to just the value ofthe the marshal brother of labor. And then this is the quantity that they hire. Okay, so for zero, where's zero labor? It's for enough. It's nothing. Okay, so the 41st the labor, we know that his value is $70 so we pay him 17. So here is 17 and then the second labor. His value is 60 over here. So 60 this point is 60. No. And then the the third labor also 60. Then the word also 60. And then, uh therefore, in the 5th 1 ISS has the value ofthe 30. So I have this here and then the 61 isthe 10 which is the hand off here in the 7th 10 So we can see that the demand a curved looks, something like thiss industry I it goes down, down and down. Where is that? We finish Christian C and D. So what happens to this thing and curved if the price of outward rises from 10 to 12 per unit so we can see that originally, we have this $10 here, right? So what if this goes up to, like, a $12? So this will change the value ofthe marginal habit of labor. So the new column is going to be the book hall of times 12. So it is all right and you being peel right here. It's like a four and then six times toiled. It's 72 and also 72 and 72 as well, and then three times 12 is 36 then one time style. His 12. So, yeah, so we can see that this curbs just goes off because now it used to be 70 now is 84 and then it's all 70 84 70 to 70 to 72 and then the third, the like 36 and then us 12 and then zero. So this grab just like, uh, magnified at at this level. But the shape iss basically the same so we can see that the demand curve just shit up, up. So that's the final answer.

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Gregory Mankiw

Principles of Economics

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Principles of Economics

Gregory MankiwPrinciples of Economics

Gregory Mankiw

Principles of Economics