Donny Saltlife shapes surfboards in Hawaii. He leases two prod...

Question

Donny Saltlife shapes surfboards in Hawaii. He leases two production machines, paying $300 each per week. He cannot increase the number of machines he leases in his contract. He can hire as many workers as he wants at a cost of $400 per week. These are his only two inputs to produce surfboards. Fill in the remaining columns in the table below.

Table showing surfboard production costs with workers, quantities, and cost categories.

Accepted Answer

Alright let's try this practice. Donnie Salt Life shapes surfboards in Hawaii. He leases 2 production machines paying $300 each per week. 300 each per week. He cannot increase the number of machines he leases in his contract, so he's stuck with that amount of machines. He can hire as many workers as he wants at a cost of $400 per week. Alright, so workers are gonna cost him $400 per week. These are his only two inputs to produce surfboards. Fill in the remaining columns in the table below, all right? So they gave us some information, right? They told us as he hires more and more workers, he's gonna have certain quantities that are gonna be output there. Cool, so let's go ahead and start here with our fixed cost. What do you think our fixed costs are gonna be? They told us 2 costs in this problem. They told us he has 2 production machines at $300 per week and he's got laborers that he's gonna hire for $400 per week. So the fixed cost is gonna be those production machines, right? And he's got 2 production machines each at 300, right? And the reason these are fixed is that no matter how many surfboards he makes, he's gonna have this same cost, right? This 300 each per week is not gonna change no matter how many surfboards he makes. So we're gonna see the fixed costs are gonna be those $300 times 2, right, because he's got 2 machines and they're each 300. So the fixed cost, it's always gonna be 600, right? 300 times 2, no matter how many surfboards he shapes, the fixed cost will always be 600, alright? Let's go about the variable cost. So now variable costs are gonna change with output, right? So the more output we make, the more we expect to spend in variable cost. So we had 2 costs in this problem. We already said that the production machines were going to be our fixed cost, right? Because that's not going to change with output, but the workers are gonna change with output, right, as we wanna make more and more surfboards we're gonna need more and more workers. So let's calculate our variable cost as the number of workers times the wage they're gonna get, right? This is gonna be our variable cost in this situation. So let's go ahead and start. At first, we've got 0 workers so 0 workers are gonna get $0. How about 1 worker? When we've got 1 worker, he's gonna earn the wage of 400, right? So it's gonna be 1 times the 400 wage and we're gonna have a variable cost of 400 there. How about 2 workers? Well now we're talking about 400 times 2, right? 2 workers so it's gonna be 800 and moving right along, 3 workers, it's gonna be 1200 right? That's 400 times 3. 4 workers is 400 times 4 which is 1600 and last but not least, 5 workers times 400. That's gonna give us 2,000 in variable cost. Right? 5 times 400. So total cost, right, total cost is just gonna be our fixed cost plus our variable cost, right? That's how we define total cost. So let's go ahead and just add across here, right? We've got our fixed cost, we've got our variable costs. Let's do it. 600 plus 0, I can do that in my head. That's 600, right? How about 600+400, that's gonna come out to a1000. 600 +800 is gonna be 1400. 600 +1200, that's 1800. 600+1600, that's 2,200 and last but not least, 2,000 +600, that's 2,600. Cool? Alright. So we've filled in quite a bit here. Now we just have to calculate average total cost and our marginal cost. So let's start here with average total cost, right, and that's just gonna be that total cost. Right? Anytime we want an average cost, we just divide by quantity, right? So it's gonna be that total cost divided by quantity. So let's start here. In the first case, we've got 600 total cost but no surfboards, right? So we can't calculate an average there, we didn't produce anything. How about when we've got one worker, we produce 8, right, where our quantity is 8. So we're gonna take our total cost of 1,000 divided by the 8 quantity and we're gonna get a $125. Right? So it's gonna be a $125 per surfboard there, average total cost. Next one, 1400 total cost divided by, what did we get there? 20 surfboards. Right? 1400 total cost divided by 20. That's gonna get our average total cost down to 70 there, right? And continuing, we've got 1800 in total cost divided by 25 surfboards this time. That gives us a total cost of 72 and let's keep it going. We've got 22100 in total costs divided by 28 and I'll round this off here to $78.57 Cool. And last 1, 26 $100 in total cost divided by 30 and that's gonna give us an average cost here of 86.6 67. Alright. Rounding it off there. Cool. So there's our average total cost just taking that total cost column divided by the quantity for that row. Alright? Let's go ahead and finish up here with our marginal, our marginal cost, right, and that's gonna just gonna be the change in the total cost over the change in the quantity, right? So we're gonna need the change in the total cost and the change in the quantity. Let's go ahead and fill that in right down here. We don't have columns for it so we're gonna need need to get calculate these. Right? Our change in total cost and our change in quantity. Right? So this is gonna be when we have 0, 1, 2, 3, 4, and 5 workers, right. So we're gonna see what happens to our quantity and our total cost. So from 0 to 1, right, we're not gonna calculate it for 0, right, because there's no quantity, no cost, and no changes there. So we gotta start from 1. At 1, we've got, our change in total cost was let's see it's gonna be the difference between these two right here, right? We started at 600 in cost and now we're at a1000 in cost, right? So our cost went from 600 to 1,000 well that's just gonna be 400 in extra cost, right? So our total cost increased by 400 there. Same again here we're gonna see we went from a 1,000 to 1400, right? Again it's gonna be 400 is our change in total cost, right? And that's because our fixed costs haven't changed. So the only thing here that's changing is our variable cost. And our variable cost is $400 per worker. So every time we add a worker, we're gonna pay an extra 400, right? So as you see as we go down here, the only increase of the total cost is 400 for each additional worker. So all the way down, we're gonna see that the change in total cost is 400 for every single additional worker, right? Our change in total cost is 400. So let's talk about change in quantity. So when we produced our 1st or when we hired our 1st worker, we got from 0 quantity up to 8, right? So our change in quantity in that first case is gonna be those 8, 8 surfboards, but what about in the second case? When we had a second worker worker, we already had 8 surfboards and now we got up to 20, right? So the 20 minuteus the 8 we already had, that's 12 more surfboards that we got from the 2nd worker. How about the next one? We were at 20, got up to 25, right? So that's 5, right? It went up by 5 that time. 25 to 28, well the difference there is 3, right? So the 4th worker adds 3 and last but not least, our 5th worker, we were at 28% and it gets us up to 30%, right? So he added an additional 2. 2830% the difference there is 2. So there we go, we've calculated our changes in total cost and our changes in quantity, all that's left is to calculate marginal cost and to do that we're just going to divide, right? All we got to do is divide the change in total cost, divided by change in quantity. Cool? Let's go ahead and do that. So the first one, remember when 0, we're not gonna have anything, right, because there's no production, we've got no quantity, we are not gonna calculate that. So how about when we've got 1 worker? We've got 400 total cost change, divided by 8, quantity change, right? So 400 divided by 8, that's gonna give us 50, right? So this last one here, we're gonna have 50 for our marginal cost. How about with 2 workers? 400 divided by 12. That one's 33.33. Alright? So the next one we've got 3 workers. We've got 405 down here. Right? 400 divided by 5, that gives us 80. Yep. 80. So our marginal cost went to 80 there. How about 400 divided by 3? That's gonna give us a $133.33. Alright? And last but not least, we've got 400 divided by 2 and that one there is 200. So we're seeing something similar to what we're used to, right? Look at our change in quantity. Our change in quantity, remember our change in quantity that was our marginal product of labor, right? How much extra are we getting by adding one more laborer, right? So in this case we saw that our change in quantity right we were getting an increase in marginal product of labor and then after 2 workers it started decreasing immediately, right? So it started going down, down, and down and notice what's happened to our marginal cost is that it decreases when that marginal product of labor was increasing and then it starts increasing when that marginal product of labor is decreasing, right? They're inversely related. As that marginal product of labor went up, the marginal cost went down and then the opposite started happening right? We started seeing those diminishing returns by adding more workers to a fixed amount of production machines, they started getting less and less efficient and that happened pretty quickly here right. This happened just after 2 workers, the marginal product started decreasing and our marginal cost started going up. Cool? Alright, let's go ahead and move on to the next one.

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