Suppose that the cost function for a commodity is (x) = 90 + x? dollars. (a) Find the marginal cost at x = 7 units. MC(7) Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 8th unit is predicted to be $ (b) Calculate C(8) - C(7) to find the actual cost of producing 1 additional unit.
Suppose that the cost function for a commodity is (x) = 90 + x? dollars. (a) Find the marginal cost at x = 7 units. MC(7) Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 8th unit is predicted to be $ (b) Calculate C(8) - C(7) to find the actual cost of producing 1 additional unit.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![**Title: Understanding Cost Functions and Marginal Cost Calculation**
**Cost Function Overview:**
Consider a commodity with a cost function given by:
\[ C(x) = 90 + x^2 \]
This equation represents the total cost \( C(x) \) in dollars to produce \( x \) units of the commodity.
**Part (a): Marginal Cost Calculation**
To find the marginal cost at \( x = 7 \) units, we need to calculate:
\[ MC(7) = \]
The marginal cost provides an estimate of the cost of producing one additional unit.
**Prediction:**
The predicted cost to produce the 8th unit is:
\[ \text{\$} \_\_\_\_\_\_\_\_\_\_\_ \]
**Part (b): Actual Cost Calculation**
Calculate the difference between \( C(8) \) and \( C(7) \) to find the actual cost of producing one additional unit:
\[ C(8) - C(7) = \]
This calculation gives the actual cost of producing the 8th unit:
\[ \text{\$} \_\_\_\_\_\_\_\_\_\_\_ \]
**Explanation:**
The difference between the predicted and actual costs can highlight inaccuracies in using marginal costs for estimation in non-linear cost functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b81583b-a567-47d2-a196-b2546011bb07%2F037ca3d4-3933-4584-9db4-d34430cf16fd%2Flbddy8_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Cost Functions and Marginal Cost Calculation**
**Cost Function Overview:**
Consider a commodity with a cost function given by:
\[ C(x) = 90 + x^2 \]
This equation represents the total cost \( C(x) \) in dollars to produce \( x \) units of the commodity.
**Part (a): Marginal Cost Calculation**
To find the marginal cost at \( x = 7 \) units, we need to calculate:
\[ MC(7) = \]
The marginal cost provides an estimate of the cost of producing one additional unit.
**Prediction:**
The predicted cost to produce the 8th unit is:
\[ \text{\$} \_\_\_\_\_\_\_\_\_\_\_ \]
**Part (b): Actual Cost Calculation**
Calculate the difference between \( C(8) \) and \( C(7) \) to find the actual cost of producing one additional unit:
\[ C(8) - C(7) = \]
This calculation gives the actual cost of producing the 8th unit:
\[ \text{\$} \_\_\_\_\_\_\_\_\_\_\_ \]
**Explanation:**
The difference between the predicted and actual costs can highlight inaccuracies in using marginal costs for estimation in non-linear cost functions.
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