To sketch the Total Revenue (TR), Total Cost (TC), and Total Profit functions in the same coordinate system, we can follow these steps. I will describe how to structure the graph since I can't provide an actual sketch.
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Coordinate System:
- The x-axis will represent the quantity of goods produced and sold (Q).
- The y-axis will represent monetary values for TR, TC, and profit (in currency units).
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Total Revenue (TR):
- Total Revenue is calculated as \( TR = P \times Q \), where P is the price per unit.
- The TR curve is usually a straight line starting from the origin (0,0), as revenue increases linearly with quantity when price is constant.
- As quantity increases, TR rises with a positive slope of P.
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Total Cost (TC):
- Total Cost includes fixed and variable costs. TC can be expressed as \( TC = FC + VC(Q) \), where FC is fixed cost and VC is variable cost depending on Q.
- The TC curve typically starts above the origin because of fixed costs. Its slope depends on variable costs, which may be constant, increasing, or decreasing depending on how production affects costs.
- If variable cost is constant, the TC will have a linear upward slope. If variable costs increase with production, the TC curve will become steeper as Q increases.
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Total Profit (TP):
- Total Profit is calculated as \( TP = TR - TC \).
- The TP curve will depend on the relationship between TR and TC.
- When TR is above TC, TP is positive. When TR is below TC, TP is negative.
- Start plotting TP by taking the vertical distance between the TR and TC curves. The TP curve typically has a peak, where the profit is maximized, and may become negative beyond a certain quantity if costs exceed revenues.
Steps to Sketch:
- Draw the Axes: Label your x-axis as Quantity (Q) and y-axis as Monetary Value.
- Plot TR: Start at (0,0) and draw a straight line upward as Q increases.
- Plot TC: Start above (0,0) at the level of fixed costs (FC) and slope it up depending on variable costs.
- Plot TP: Identify where TR is above TC and shade the area between them as profit. Draw a curve starting at the origin, peaking when TR exceeds TC the most, and eventually dropping off as TC may surpass TR.
Key Points to Take Note:
- TR curve has a linear slope if the price is constant.
- TC curve may start above the origin due to fixed costs and has a slope based on the variable costs.
- TP curve may initially rise as profits increase but will eventually decline if costs exceed revenues.
Label and Analyze:
- Clearly label each curve (TR, TC, and TP).
- Analyze where profit is maximized (the peak of the TP curve) and note the break-even point where TR equals TC.