Clean "n' Shine is a competitor to Spotless Car Wash. Like...

Clean "n' Shine is a competitor to Spotless Car Wash. Like Spotless, it must pay 150 dollar per day for each automated line it uses. But Clean "n' Shine has been able to tap into a lower-cost pool of labor, paying its workers only 100 dollar per day. Clean "n' Shine's production technology is given in the following table. To determine its short-run cost structure, fill in the blanks in the table. a. Over what range of output does Clean "n' Shine experience increasing marginal returns to labor? Over what range does it experience diminishing marginal returns to labor? b. As output increases, do average fixed costs behave as described in the text? Explain. c. As output increases, do marginal cost, average variable cost, and average total cost behave as described in the text? Explain. d. Looking at the numbers in the table, but without drawing any curves, is the relationship between $M C$ and $A V C$ as described in the text? What about the relationship between $M C$ and $A T C$ ?

Clean "n' Shine is a competitor to Spotless Car Wash. Like Spotless, it must pay 150 dollar per day for each automated line it uses. But Clean "n' Shine has been able to tap into a lower-cost pool of labor, paying its workers only 100 dollar per day. Clean "n' Shine's production technology is given in the following table. To determine its short-run cost structure, fill in the blanks in the table.
a. Over what range of output does Clean "n' Shine experience increasing marginal returns to labor? Over what range does it experience diminishing marginal returns to labor?
b. As output increases, do average fixed costs behave as described in the text? Explain.
c. As output increases, do marginal cost, average variable cost, and average total cost behave as described in the text? Explain.
d. Looking at the numbers in the table, but without drawing any curves, is the relationship between $M C$ and $A V C$ as described in the text? What about the relationship between $M C$ and $A T C$ ?

Key Concepts

Average Total Cost

Average total cost is calculated by dividing the total cost by the number of units produced. This measure integrates both fixed and variable costs and provides insight into the per-unit cost of production. It is useful for assessing scale economies and for making pricing and output decisions, particularly when comparing with marginal cost.

Cost Curve Relationships

The relationships between marginal cost and average costs (both average variable cost and average total cost) are fundamental in cost analysis. Specifically, the marginal cost curve typically intersects the average cost curves at their minimum points, reflecting how marginal changes influence average measures. This relationship helps explain the behavior of cost curves and is key for understanding firms’ decisions regarding production levels and cost management.

Increasing and Diminishing Marginal Returns

This concept describes how the marginal product of an input such as labor initially increases with additional units of input (increasing marginal returns), but eventually, due to factors like congestion or limited fixed inputs, the additional output from each new unit of input begins to decrease (diminishing marginal returns). Understanding this concept is critical for explaining changes in marginal cost and overall efficiency in the short run.

Average Variable Cost

Average variable cost is the variable cost per unit of output, obtained by dividing the total variable cost by the quantity produced. It is an important measure for analyzing the efficiency of production and for understanding how variable costs contribute to overall cost behavior as output increases.

Variable Costs

Variable costs change directly with the level of output produced. These costs, which include expenses like wages for labor, increase as production increases and decrease as production declines. Understanding variable costs is vital for evaluating the marginal and average cost measures since they affect the cost structure differently from fixed costs.

Total Cost

Total cost is the sum of fixed and variable costs incurred during production. It represents all the expenditures a firm must make to produce a given level of output. Analyzing total cost helps in understanding the overall cost structure and in making decisions regarding production and pricing.

Marginal Cost

Marginal cost is the additional cost incurred by producing one more unit of output. It is calculated as the change in total cost associated with a unit change in output. This concept is important in production theory and cost management because it helps determine the optimal level of production and how costs evolve as output changes.

Short?Run Production Function

This concept refers to the production process in which at least one factor of production, such as capital or plant size, is fixed, while other factors, such as labor, can be varied. It provides the framework for analyzing how changes in variable inputs influence output, and it is essential for understanding cost behavior, especially when dealing with fixed and variable components in the short run.

Fixed Costs

Fixed costs are expenses that do not change with the level of output produced over the short run. These costs, such as rental fees or per-line payments, remain constant regardless of how much is produced. They are crucial for understanding the baseline costs that a firm incurs and play a significant role in the calculation of total and average cost measures.

Transcript

0:00 All right.

00:01 So we start here with a table that you will also see in question 8 of clean and shine and their cost table.

00:12 And so what they want us to do here is fill out the rest of the table with the information that one unit of capital, right, one automated lawn costs $150 per day.

00:24 And one unit of labor, one worker, will cost $100 per day.

00:27 So, first thing that we can definitely do is fill up our total fixed cost, total variable cost, and then total cost, after which we can figure out our average fixed cost, average variable cost, average total cost, and our marginal cost.

00:44 So, knowing that we have one unit of capital along the whole line, we know that our total fixed cost will be $150 throughout this entire table.

01:00 50, 150, and 150.

01:04 And then knowing that one worker costs $100 per day, every time that we add a worker, we're adding $100 to our total variable cost.

01:14 So that is not 100, that is 200, 300, 400, and so forth.

01:29 And we know here that our total cost is merely the addition of our total variable cost and our total fixed cost.

01:41 So then we can go ahead and fill out the rest of that as well.

01:49 250 and 150.

01:52 Then average fixed cost, as we know, is total fixed cost divide by output.

01:57 Average variable cost will be total variable cost divided by output.

02:02 Average total cost would then be total cost divide by output.

02:07 But we could also solve by doing average fixed cost.

02:09 The bot plus, excuse me, average variable cost.

02:16 If there's zero output, there's not really an average there.

02:20 Then, as we move forward, average fixed cost is equal to five.

02:27 Average variable cost is equal to 3 .33.

02:37 And so our average total cost will be 8 .33.

02:40 We know then for the next row for 70 units of output, our average fixed cost, we'll go down 2 .14, average variable cost, 2 .86, and then our average total cost being equal to 5.

03:05 Doing this with the next column, or next row, excuse me, average fixed cost being 1 .25, our average variable cost being 2 .5.

03:17 Then our average total cost being 3 .75, doing this with the row of 160, our average fixed cost going 0 .94, average variable cost, again being 2 .5, and then our average total cost being 3 .44.

03:41 Then for our relf 190, our average fixed cost being .79, our average variable cost being 2 .63, then our average total cost being 3 .42.

04:03 Then finally, our average fixed cost being .71.

04:09 Our average variable cost being 2 .86, then our average total cost being 3 .57.

04:26 And finally, we can figure out the marginal cost for all of this, which we then can find through how many additional units of output, right? example from zero to 30, we're adding one worker.

04:40 So that's $100.

04:41 So marginal cost.

04:42 So marginal cost.

04:43 Would be 100 over 30 or 3 .3 .3.

04:51 Then our next one would be $100 for 40 additional units of output, marginal cost of 2 .5.

05:04 Then we have 50 additional units of output for $100, so it's two.

05:10 After that, again, 40 units of output increase, again, 30 units of output increase...

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