Consider the following cost functions.
a. Find the avera...

Question

Consider the following cost functions.

a. Find the average cost and marginal cost functions.

C(x) = 1000+0.1x, 0≤x≤5000, a=2000

Accepted Answer

Below there, today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Consider the cost function given by C of Y is equal to 500 plus 0.2 Y, where 0 is less than or equal to Y and Y is less than or equal to 3000. Determine the average cost and marginal cost functions. Awesome. So it appears for this particular problem we're asked to solve for two separate answers. We're asked to figure out the average cost. That's our first answer, and our second answer is the marginal cost. So we're trying to figure out the average cost function and the marginal cost function. And those are two final answers that we're trying to ultimately solve for. So first off, what we're trying to do is we're trying to determine the average cost function. So let's focus our attention on solving for the average cost function first. So in order to do that, let us define our known variables. Let us know that we're told that the cost function, which is going to be C of Y, and C of Y, as we should recall, once again is equal to 500, and then we need to take 500, and we need to add. 0.2 Y. and we also need to note and recall that the output level is Y. Fantastic. So now we need to note that the average cost function will be given by A C of Y is going to be equal to C of Y divided by Y. So now we need to substitute in the cost function into our average cost function equation. So when we do that, we will find that it's equal to 500 + 0.2 Y divided by Y, and that is our final answer for A C of Y. Hooray, we did it. So, so AC of Y. Denotes our once again our average cost function, and it turns out that it's going to be equal to 500 + 0.2 Y divided by Y. Fantastic. So we found one of our answers. So now we need to find the marginal cost function. So in order to determine the marginal cost function, let us first define our known variables. So once again, we know the cost function, which is C of Y is equal to 500 plus 0.2 Y. And we also know the output level, and once again the output output level is Y. So now all we need to do is we need to recall and use the marginal cost function, and in order to figure out the marginal cost function, we need to recall and note that it will be the derivative of the cost function with respect to Y. So we can state that MC of Y, the marginal cost function is going to be equal to DC of Y by DY. So we need to differentiate the cost function. So MC of Y is equal to D by DY of 500 + 0.2 Y. And when we take the derivative, we will find that it's equal to 0.2. Fantastic. So that's it. Those are our final two answers. Hooray, we did it. So to quickly recap here, our final two answers, without a doubt, have to be. Once again, our, so we have two answers. So for our average cost function, which is AC of Y, is going to be equal to 0.2 Y plus 500 divided by Y, and our marginal cost function, which is MC of Y, is going to be equal to 0.2. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Consider the following cost functions.
a. Find the average cost and marginal cost functions.
C(x) = 1000+0.1x, 0≤x≤5000, a=2000

Key Concepts

Average Cost Function

Marginal Cost Function

Cost Function

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