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\begin{table}

\captionsetup{labelformat=empty}

\caption{The Cost of and Return on Pie Production}


Pies produced per day		Total costMarginal costTotal revenueMarginal revenueProfit

0		\$0.00\$0.00--\$0.00

1		\$1.00\$1.00\$10.00\$10.00\$9.00

2		\$1.50\$0.50\$20.00\$10.00\$18.50

3		\$1.75\$0.25\$30.00\$10.00\$28.25

4		\$2.25\$0.50\$40.00\$10.00\$37.75

5		\$3.50\$1.25\$50.00\$10.00\$46.50

6		\$5.00\$1.50\$60.00\$10.00\$55.00




\end{table}



What most likely will happen if the pie maker bakes a seventh pie?


AThe marginal cost will most likely decrease to \$1.00.
BThe marginal cost will most likely increase to \$2.00.
CThe marginal revenue will most likely decrease to \$8.00.
DThe marginal revenue will most likely increase to \$12.00.

Verified Answer :

  • Marginal revenue remains constant at \(\$10.00\), indicating a competitive price.
  • Marginal cost follows an increasing trend after the third pie, rising from \(\$0.25\) to \(\$1.50\) by the sixth pie.
  • Following this upward trend, the marginal cost of the seventh pie is most likely to increase to \(\$2.00\).
  • Final Answer: \(\boxed{\text{The marginal cost will most likely increase to \$2.00}}\)

Explanation

  1. Analyzing Cost and Revenue Trends

To analyze the economics of producing a seventh pie, we first look at the trends for Marginal Cost (MC) and Marginal Revenue (MR) in the provided table. Marginal cost represents the additional cost of producing one more unit, calculated by subtracting the total cost of the previous quantity from the total cost of the current quantity: \(MC = TC_Q - TC_{Q-1}\). Marginal revenue is the additional income from selling one more unit, which remains constant at \(\$10.00\) per pie in this scenario.

  1. Evaluating Marginal Cost Behavior

Looking at the data for Marginal Cost:

  • For \(Q=1\): \(\$1.00\)
  • For \(Q=2\): \(\$0.50\)
  • For \(Q=3\): \(\$0.25\)
  • For \(Q=4\): \(\$0.50\)
  • For \(Q=5\): \(\$1.25\)
  • For \(Q=6\): \(\$1.50\)

The marginal cost decreased initially until the third pie, but then began a clear upward trend from the third to the sixth pie (\(0.25 \rightarrow 0.50 \rightarrow 1.25 \rightarrow 1.50\)). This upward trend is characteristic of diminishing returns, where each additional unit becomes increasingly expensive to produce as capacity is reached. Given that Marginal Revenue is constant at \(\$10.00\), we expect the Marginal Cost to continue its upward trajectory as the firm approaches its production limit.

  1. Selecting the Likely Outcome

Comparing our observations to the given options:

  • The marginal revenue is stable at \(\$10.00\), making decreases or increases to \(\$8.00\) or \(\$12.00\) unlikely in this market.
  • The marginal cost shows a consistent increasing trend after the third unit (\(0.25, 0.50, 1.25, 1.50\)). An increase to \(\$2.00\) for the seventh pie is the most logical continuation of this pattern.
  • A decrease to \(\$1.00\) contradicts the established upward trend of marginal costs.

Therefore, the most likely outcome is that the marginal cost will increase to \(\$2.00\).

Examples

Consider a small bakery owner deciding whether to hire an extra baker. If the cost of the first few extra bakers is low but then begins to rise due to limited oven space and congestion in the kitchen, the owner observes an increasing marginal cost. By tracking these costs, the business owner can determine the optimal production level—the point where the cost to produce one more unit equals the revenue brought in by that unit—to maximize overall profit.

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