Quantity Of Cars And Total Costs
Quantity Of Carstotal Cost0500000154000025600003570000459000
Calculate the fixed cost, marginal cost, variable cost, average variable cost, average total cost, and average fixed cost for the manufacturer at various levels of output based on the provided data.
Paper For Above instruction
The analysis of production costs is essential for understanding a manufacturer’s cost structure and making informed decisions regarding production levels, pricing, and profitability. This paper examines a manufacturer’s total cost at different output levels, with specific focus on determining fixed costs, marginal costs, variable costs, average costs, and the relationships between these metrics.
Given Data:
| Quantity of Cars (Q) | Total Cost (TC) |
|---|---|
| 0 | $500,000 |
| 1 | $540,000 |
| 2 | $560,000 |
| 3 | $570,000 |
| 4 | $590,000 |
| 5 | $620,000 |
| 6 | $660,000 |
| 7 | $720,000 |
| 8 | $800,000 |
| 9 | $920,000 |
| 10 | $1,100,000 |
a. Fixed Cost (FC)
The fixed cost represents expenses that do not change with the level of output. Typically, fixed costs are observed at zero output, as they are costs incurred regardless of production activity. Based on the data, at zero output, the total cost is $500,000, indicating that
Fixed Cost (FC) = $500,000
b. Marginal Cost (MC) at each level of output
The marginal cost is calculated as the increase in total cost resulting from producing one additional unit of output. It can be computed using the difference in total costs between consecutive outputs:
- MC between 0 and 1 units: ($540,000 - $500,000) = $40,000
- MC between 1 and 2 units: ($560,000 - $540,000) = $20,000
- MC between 2 and 3 units: ($570,000 - $560,000) = $10,000
- MC between 3 and 4 units: ($590,000 - $570,000) = $20,000
- MC between 4 and 5 units: ($620,000 - $590,000) = $30,000
- MC between 5 and 6 units: ($660,000 - $620,000) = $40,000
- MC between 6 and 7 units: ($720,000 - $660,000) = $60,000
- MC between 7 and 8 units: ($800,000 - $720,000) = $80,000
- MC between 8 and 9 units: ($920,000 - $800,000) = $120,000
- MC between 9 and 10 units: ($1,100,000 - $920,000) = $180,000
c. Variable Cost (VC) for each level of output
The variable cost is derived by subtracting the fixed cost from the total cost at each level, because fixed costs are constant, and variable costs change with output. Thus:
VC = TC - FC
- Q=1: $540,000 - $500,000 = $40,000
- Q=2: $560,000 - $500,000 = $60,000
- Q=3: $570,000 - $500,000 = $70,000
- Q=4: $590,000 - $500,000 = $90,000
- Q=5: $620,000 - $500,000 = $120,000
- Q=6: $660,000 - $500,000 = $160,000
- Q=7: $720,000 - $500,000 = $220,000
- Q=8: $800,000 - $500,000 = $300,000
- Q=9: $920,000 - $500,000 = $420,000
- Q=10: $1,100,000 - $500,000 = $600,000
d. Average Variable Cost (AVC) for each output
The AVC is calculated as:
AVC = VC / Q
| Quantity (Q) | VC | AVC |
|---|---|---|
| 1 | $40,000 | $40,000 / 1 = $40,000 |
| 2 | $60,000 | $30,000 |
| 3 | $70,000 | $23,333 |
| 4 | $90,000 | $22,500 |
| 5 | $120,000 | $24,000 |
| 6 | $160,000 | $26,667 |
| 7 | $220,000 | $31,429 |
| 8 | $300,000 | $37,500 |
| 9 | $420,000 | $46,667 |
| 10 | $600,000 | $60,000 |
e. Average Total Cost (ATC) for each output
The ATC is obtained by dividing total cost by quantity:
ATC = TC / Q
| Quantity (Q) | Total Cost (TC) | ATC |
|---|---|---|
| 1 | $540,000 | $540,000 / 1 = $540,000 |
| 2 | $560,000 | $280,000 |
| 3 | $570,000 | $190,000 |
| 4 | $590,000 | $147,500 |
| 5 | $620,000 | $124,000 |
| 6 | $660,000 | $110,000 |
| 7 | $720,000 | $102,857 |
| 8 | $800,000 | $100,000 |
| 9 | $920,000 | $102,222 |
| 10 | $1,100,000 | $110,000 |
f. Average Fixed Cost (AFC) for each output
The AFC is computed by dividing the fixed cost by the quantity:
AFC = FC / Q
| Quantity (Q) | Fixed Cost (FC) | AFC |
|---|---|---|
| 1 | $500,000 | $500,000 / 1 = $500,000 |
| 2 | $500,000 | $250,000 |
| 3 | $500,000 | $166,667 |
| 4 | $500,000 | $125,000 |
| 5 | $500,000 | $100,000 |
| 6 | $500,000 | $83,333 |
| 7 | $500,000 | $71,429 |
| 8 | $500,000 | $62,500 |
| 9 | $500,000 | $55,556 |
| 10 | $500,000 | $50,000 |
Conclusion
This detailed analysis reveals that the fixed cost for the manufacturer remains constant at $500,000 across all output levels. The marginal costs fluctuate significantly, especially as output increases, indicating variable production efficiencies and potential economies or diseconomies of scale. The variable, average variable, and average total costs vary accordingly, with average costs generally decreasing initially and then rising at higher output levels due to increasing marginal costs. The average fixed cost decreases steadily as output increases, reflecting the fixed cost being spread over more units.
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