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A bakery operating in competitive markets sells itsoutput for $\$ 20$ per cake and hires labor at $\$ 10$ perhour. To maximize profit, it should hire labor until themarginal product of labor isa. 1$/ 2$ cake per hour.b. 2 cakes per hour.c. 10 cakes per hour.d. 15 cakes per hour.

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a. 1$/ 2$ cake per hour.

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Chapter 18

The Markets for the Factors of Production

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So here we're gonna be talking about the equilibrium that firms are gonna try to find. And so the kind of rule of thumb here is that we're gonna have the wage being equal to the value off the marginal product of labor. So V w equals V m pl so within that, we can break down value of marginal product of labor into two parts. So that's gonna be the price. So basically each good cells for how much and the marginal product of labor, which, um, different color, which we can kind of describe as if we hire one more worker. How much more output do they produce? So when this question is asking us these things, we already have a bunch of pieces of the puzzle here. So we know that the wage is $10 per hour, and then we know that we have the price equal to $20 per cake. Right? So basically, the way we're gonna balance this out is the place where our ah, marginal product of labor. So if we were to hire one more Riker, where is that gonna be equal to? Where is that gonna make this function work? so times mpl So just do a little bit of simple algebra here and rearrange that and you get, um, our m p l is going to be equal to one half. Sorry, I'm Glitch Tup there 1/2 on. And so our answer here is gonna be a And basically what that saying is that if we were to hire who put this in words, it's saying for every one additional worker, we're going to get half a cake extra. Uh, and that's the point where our wages gonna be equal to the value of the marginal product of labor. So think about it. Like, um, you hire one more rooker. Um, so this here is gonna be our equilibrium, and it's if you hire one more workers, they're gonna make half a cake, and half a cake is worth $10 which is exactly what you're paying them. So that's why it's out equally

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