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Chapter 17: Problem 648

The National Widget Corporation currently holds a five-year lease on their factory, on which they have four more years left before the lease runs out. Beginning this month, the landlord has been allowed to pass along a \(\$ 100\) per month "fuel adjustment surcharge." If, every month, NWC's economists (by some miracle) are able to chart their cost curves for the upcoming month, how would the cost curves have changed to reflect this fuel surcharge, assuming that no other factors have changed?

Short Answer

Expert verified
To account for the new \$100 fuel surcharge, NWC's fixed cost function is updated by adding \$100 to the current fixed costs: New FC(q) = Old FC(q) + $100. Consequently, their total cost function (TC) changes: New TC(q) = (Old FC(q) + $100) + VC(q). This causes the total cost curve to shift vertically upwards by \$100, reflecting the surcharge's added expense. Variable costs remain unchanged.

Step by step solution

01

Identify the current cost curves

Before the fuel surcharge is implemented, NWC's economists will already have cost curves for the upcoming month that reflect the total costs of producing different quantities of widgets. These curves could be expressed as total cost (TC), fixed cost (FC), and variable cost (VC) functions depending on the number of widgets produced (q).
02

Understand the fuel surcharge

The fuel surcharge is an additional \$100 per month expense, which means it gets added to NWC's costs every month. Since it's a constant value that does not change depending on the number of widgets produced, we can consider it to be a fixed cost.
03

Adjust the fixed costs

Since the fuel surcharge can be considered as an additional fixed cost, we can incorporate it by updating the fixed cost function (FC) by adding \$100 to the current fixed costs: New FC(q) = Old FC(q) + $100
04

Update the total cost function

Now that we have adjusted the fixed cost function, we should update the total cost function as well. The total cost function is the sum of fixed cost and variable cost functions: TC(q) = FC(q) + VC(q) Since we updated the fixed cost function, we can now write the new total cost function: New TC(q) = New FC(q) + VC(q) By replacing New FC(q) by the expression we found in Step 3: New TC(q) = (Old FC(q) + $100) + VC(q)
05

Interpret the result

The new total cost function, New TC(q), incorporates the fuel adjustment surcharge by adding \$100 to NWC's fixed costs. This means that, for every month, the total cost will increase by \$100 due to the fuel surcharge, affecting NWC's cost curves. Since variable costs remain unchanged, the change in cost curves will result in a vertical shift upwards by \$100, reflecting the extra cost from the surcharge.

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Most popular questions from this chapter

Given the information in Table 1, construct a table showing the average and marginal costs (per thousand units) at each level of output. $$ \begin{aligned} &\text { Table } 1\\\ &\begin{array}{|c|c|} \hline \text { Autos produced (thousands) } & \text { Total Cost } \\ \hline 10 & \$ 50,000,000 \\ \hline 11 & 56,000,000 \\ \hline 12 & 62,500,000 \\ \hline 13 & 69,500,000 \\ \hline 14 & 79,000,000 \\ \hline 15 & 90,000,000 \\ \hline \end{array} \end{aligned} $$

Given: \(\mathrm{TC}=\mathrm{FC}+\mathrm{VC}\) prove that: \(\quad \mathrm{ATC}=\mathrm{AFC}+\mathrm{AVC}\)

Given the total cost and total fixed cost data of table 1 , calculate the total variable cost incurred at each level of output. $$ \begin{aligned} &\text { Table } 1\\\ &\begin{array}{|l|l|l|} \hline \text { Quantity Produced } & \text { Total fixed cost } & \text { Total cost } \\ \hline 1 & \$ 1000 & \$ 1500 \\ \hline 2 & 1000 & 1950 \\ \hline 3 & 1000 & 2350 \\ \hline 4 & 1000 & 2700 \\ \hline 5 & 1000 & 3000 \\ \hline 6 & 1000 & 3300 \\ \hline 7 & 1000 & 3650 \\ \hline 8 & 1000 & 4000 \\ \hline 9 & 1000 & 4400 \\ \hline 10 & 1000 & 4900 \\ \hline \end{array} \end{aligned} $$

Mr. Brennan owns an open field adjacent to his house. The coach of the local high school football team offered Mr. Brennan \(\$ 250\) to rent the field from him for his team's summer football drills. Mr. Brennan could also grow vegetables on the field. The cost of seed, fertilizer, and hiring neighborhood teenagers to plant and harvest the field he estimates would be \(\$ 200\) and \(\mathrm{Mr}\). Brennan expects to receive \(\$ 500\) if he sold the vegetables. What are the explicit and implicit costs to Mr. Brennan of growing vegetables, and will he choose to grow vegetables or rent the field?

Suppose that the average cost of mining a ton of coal varies with the total weight of coal mined each day in the way shown in Table 1 . $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \text { Tons mined } & 100 & 101 & 102 & 103 & 104 & 105 \\ \hline \text { Average Cost per Ton } & \$ 300 & \$ 299 & \$ 298 & \$ 297 & \$ 296 & \$ 295 \\ \hline \end{array} $$ Compute the marginal cost at each level of production of mining a ton of coal.
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