Let's analyze and find the missing data step-by-step based on the provided cost table and formulas. --- # Step 1: Understand the abbreviations and formulas | Abbreviation | Formula / Description | |----------------|------------------------| | TC | Total Cost | | FC | Fixed Cost | | VC | Variable Cost | | MC | Marginal Cost | | ATC | Average Total Cost | | AFC | Average Fixed Cost | | AVC | Average Variable Cost | Formulas: - \( TC = FC + VC \) - \( MC = \frac{\Delta TC}{\Delta Q} \) - \( ATC = \frac{TC}{Q} \) - \( AFC = \frac{FC}{Q} \) - \( AVC = \frac{VC}{Q} \) --- # Step 2: Fill in known data and observe patterns | Q | TC | FC | VC | MC | ATC | AFC | AVC | |---|-----|-----|-----|----|-----|-----|-----| | | | | | | | | | | 1 | 6 | | | | | | | | 2 | 90 | | 12 | | | | | | 3 | | 36 | | 27 | | | | | 4 | | | 27 | 33 | 15.75 | | | | 5 | | | 39 | 12 | | | | | 6 | | | | | | | | --- # Step 3: Find fixed cost (FC) At \( Q= \), total cost \( TC= \), but no data provided. At \( Q=1 \): \[ ATC = \frac{TC}{Q} \Rightarrow \text{But } ATC \text{ is not given at } Q=1. \] At \( Q=2 \): \[ TC = 90 \] Since \( VC = 12 \) at \( Q=2 \): \[ FC = TC - VC = 90 - 12 = 78 \] Assuming fixed cost remains constant: \[ FC = 78 \] --- # Step 4: Calculate total cost at other quantities At \( Q=3 \): \[ TC = FC + VC = 78 + \text{(unknown VC at Q=3)}. \] But from the table, \( VC \) at \( Q=3 \) is 36 (given). So: \[ TC = 78 + 36 = 114 \] Check \( ATC \) at \( Q=3 \): \[ ATC = \frac{114}{3} = 38 \] --- # Step 5: Find \( MC \) at \( Q=3 \) From the data at \( Q=2 \) and \( Q=3 \): \[ MC = \frac{\Delta TC}{\Delta Q} = \frac{114 - 90}{3 - 2} = \frac{24}{1} = 24 \] But the table indicates \( MC=27 \) at \( Q=3 \), which suggests the previous calculation is approximate or the data is inconsistent. Alternatively, accept the given \( MC=27 \) at \( Q=3 \). Given the inconsistency, proceed with the provided data. --- # Step 6: Fill in missing total costs and variable costs At \( Q=4 \): \[ VC = 27 \] Total cost: \[ TC = FC + VC = 78 + 27 = 105 \] Check \( ATC \): \[ ATC = \frac{105}{4} = 26.25 \] --- # Step 7: Find total cost at \( Q=5 \): \[ VC = 39 \] \[ TC = 78 + 39 = 117 \] Calculate \( ATC \): \[ ATC = \frac{117}{5} = 23.4 \] --- # Step 8: Find total cost at \( Q=6 \): \[ VC \] is missing, but \( MC=12 \) from the table, and previous \( VC \) at \( Q=5 \) is 39. Using \( MC = \frac{\Delta TC}{\Delta Q} \): \[ \Delta TC = MC \times \Delta Q = 12 \times 1 = 12 \] Total cost at \( Q=6 \): \[ TC_{6} = TC_{5} + 12 = 117 + 12 = 129 \] Variable cost at \( Q=6 \): \[ VC_{6} = TC_{6} - FC = 129 - 78 = 51 \] --- # **Summary of completed table:** | Q | TC | FC | VC | MC | ATC | AFC | AVC | |---|------|------|------|-----|--------|-------|-------| | | | 78 | | | | | | | 1 | 6 | 78 | -72 | 6 | 6.00 | 78/1=78 | N/A (Q=1) | | 2 | 90 | 78 | 12 | 84 | 45.00 | 78/2=39 | 12/2=6 | | 3 | 114 | 78 | 36 | 27 | 38.00 | 78/3=26 | 36/3=12 | | 4 | 105 | 78 | 27 | 33 | 26.25 | 78/4=19.5| 27/4=6.75 | | 5 | 117 | 78 | 39 | 12 | 23.4 | 78/5=15.6| 39/5=7.8 | | 6 | 129 | 78 | 51 | 12 | 21.5 | 78/6=13 | 51/6=8.5 | --- # **Answer to the question:** ### 1. How many units should the company produce if market price \( P = 37 \)? - Profit-maximizing or production where \( P = MC \). - At \( Q=3 \), \( MC=27 \) (less than 37), at \( Q=4 \), \( MC=33 \) (less than 37), at \( Q=5 \), \( MC=12 \) (less than 37), at \( Q=6 \), \( MC=12 \). - Since \( MC \) at \( Q=4 \) is 33, which is less than 37, and at \( Q=3 \) is 27, which is less than 37, the company should produce as long as \( MC \leq P \). - The next \( MC \) at \( Q=6 \) is 12, still less than 37, so production can continue up to the maximum quantity where \( MC \leq P \). - The company should produce **6 units** as at \( Q=6 \), \( MC=12 \), which is less than 37, and since \( MC \) is increasing, the profit-maximizing quantity is at the highest \( Q \) where \( MC \leq P \). **Final answer:** > **The company should produce 6 units.** --- ### 2. Profit Calculation: Profit \( = \text{Total Revenue} - \text{Total Cost} \) \[ TR = P \times Q = 37 \times 6 = 222 \] \[ TC = 129 \] \[ \text{Profit} = 222 - 129 = \boxed{93} \] --- # **Final answers:** - **Production quantity:** **6 units** - **Profit:** **\$93**

# Explanation of Cost Terms ## Total Cost (TC) Total Cost is the overall expense incurred in production, combining both fixed and variable costs. ## Fixed Cost (FC) Fixed Cost remains constant regardless of production output, covering expenses like rent and salaries. ## Variable Cost (VC) Variable Cost changes with production levels, including costs for materials and labor directly tied to output. ## Marginal Cost (MC) Marginal Cost represents the additional cost incurred by producing one more unit of output. ## Average Total Cost (ATC) Average Total Cost is the total cost divided by the number of units produced, reflecting cost efficiency. ## Average Fixed Cost (AFC) Average Fixed Cost is the fixed cost per unit produced, decreasing as production increases. ## Average Variable Cost (AVC) Average Variable Cost is the variable cost per unit produced, indicating how variable expenses scale with output.