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Nimbus, Inc., makes brooms and then sells them door-to-door. Here is the relationship between the number of workers and Nimbus's output during a given day: a. Fill in the column of marginal products. What pattern do you see? How might you explain it? b. A worker costs \$100 a day, and the firm has fixed costs of \$200. Use this information to fill in the column for total cost. c. Fill in the column for average total cost. (Recall that $\textit{ATC = TC/Q.}$) What pattern do you see? d. Now fill in the column for marginal cost. (Recall that $\textit MC= \Delta TC/\Delta Q.$) What pattern do you see? e. Compare the column for marginal product with the column for marginal cost. Explain the relationship. f. Compare the column for average total cost with the column for marginal cost. Explain the relationship.

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00:06

Yi Chun L.

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this is their resulting table. The problem gives you the first two column, and you need to calculate or fill in the next four columns. Yes, the marginal product is, as the name suggests, is the marginal change in output. So the reason why I get 20 year because I take 20 year and subtract minus zero under above row why I get 30 here? Because I take 50 minus 20 and I do the same. Subtract 50 from 90 to get 40. That is part of a You can repeat the whole process to make the whole column and for part B u N calculate total cost now total cost is the sum fixed costs and variable cost. The problem gives you a fixed cost of 200. That's why you have 200 right here. Variable cost is labor cost. A worker cost 100 a day, so you need to add over on the top of fixed costs. You need to add 100 times the number of workers and because the number of workers increase by one from here to here. So you have, um, with one worker. The total cost is 200 plus 100 which is 300 with two workers, is 300 plus 100 to get 400 and you do the same to, um, the rest of the column part. See, you will need to calculate average total cost. An average total cost is just total cost divided by the number of output. Okay, you have 15 here because you take 300 divided by 20. Now, this 20 Sorry. And you get eight here because you take 400 divided by 50. You would do the same for the rest of the column. And lastly, you have marginal cost. Let's use this color. This is the formula for marginal cost. It is the change of total cost divided by the change in total output. You get five here because yeah, the change in total cost for one worker is 100. And the chain for output from one from zero worker to one worker is 20. Here you have 3.33 Because total costs change from 300 to 400 that is a change of 100. Total output changed from 20 to 50. That is a change of 30. And do the math. You have 3.33 you will do the same. You will repeat the process to finish the whole table. Okay, now, given that you have finished the table, we can make some observation regarding the Parton's of the cost. Continue to part A. You can see that marginal product rises at first, then declines happy because of diminishing marginal product. Part B. There is no question for the pattern of total cost part c. You can see that average total cost. Did I write ABC initially should be a T C. Right Average Total cost is you shape like this. When quantity is low, average total cost declines as quantity rises and when quantity is high, average total cost rises as quantity rises for D. Marginal cost is also U shape, but marginal cost rises steeply as output increases. This is due to diminishing marginal product for party. You can tell that when marginal product is rising, marginal cost is falling and vice versa. Last part f. You can compare the column for average total cost with the column for marginal costs and explain the relationship. Yeah, what you can tell is that when marginal cost is less than average total cost average Total cost. ISS falling The cost of the last unit produced caused the average down when marginal cost is greater than average. Total cost average total cost is rising because the cost of the last unit produced pushes the average up yeah.

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