5. A firm's marginal cost of production is constant at $5 per unit, and its fixed costs are $20. Draw its total, average variable and average costs.
Marginal Cost (MC): $5 per unit
Fixed Cost (FC): $20
Total Cost (TC): $25
Average Variable Cost (AVC): $5
FC is always going to be constant at $20; however, VC is the change in cost as an increase in cost of product to produce more.
To draw the total, average variable, and average costs, we need to understand the relationships between these costs.
Total Cost (TC) is the sum of the Fixed Cost (FC) and the Variable Cost (VC). In this case, the FC is constant at $20, and the VC is the product of the Marginal Cost (MC) and the quantity produced.
So, we can calculate the Variable Cost (VC) as follows:
VC = MC * Quantity
However, in this question, we are not provided with the quantity produced. We can create a table and assume different quantities to calculate the VC and TC for each quantity.
Let's assume we produce 0, 5, 10, 15, and 20 units.
Quantity | MC | VC | TC
0 | $5 | $0 | $20
5 | $5 | $25 | $45
10 | $5 | $50 | $70
15 | $5 | $75 | $95
20 | $5 | $100 | $120
Now that we have calculated the Variable Cost (VC) and the Total Cost (TC) for each quantity, we can draw the cost curves.
To draw the costs on a graph, we will plot the quantity on the x-axis and the cost on the y-axis.
The Total Cost (TC) curve will start at $20 (FC) and will increase by $5 (MC) for each unit produced. So, it will be a straight line with a positive slope, passing through the point (0, $20).
The Average Variable Cost (AVC) is calculated by dividing the Variable Cost (VC) by the quantity produced. As the MC is constant at $5, the AVC will also be constant at $5.
The Average Cost (AC) or Average Total Cost (ATC) is calculated by dividing the Total Cost (TC) by the quantity produced. As we calculated earlier, the TC increases when the quantity increases, but the rate at which it increases will decrease as the quantity increases. Hence, the AC (or ATC) curve will be U-shaped, with the lowest point indicating the minimum average cost.
So, to summarize, the curves can be drawn as follows:
- Total Cost (TC) curve: A straight line with a positive slope, passing through the point (0, $20).
- Average Variable Cost (AVC) curve: A horizontal line at $5 throughout the graph.
- Average Cost (AC) or Average Total Cost (ATC) curve: U-shaped, with the lowest point indicating the minimum average cost.
Note: The curves will differ for different quantities produced, but the relationships will remain the same.