A computer company produces affordable, easy-to-use home computer systems and has fixed costs of $250. The marginal cost of producing computers is $700 for the first computer, $250 for the second, $300 for the third, and $350 for the fourth, $400 for the fifth, $450 for the sixth, and $500 for the seventh.
At what price is the zero-profit point?
I know that the zero-profit point formula is:
Price per unit x number of units = Fixed costs + (variable costs per unit x number of units)
Without the price per unit, how do I figure this out?
In this case, you can use the marginal cost of producing each computer to calculate the total variable cost. The total variable cost is the sum of the marginal costs for each computer. In this case, the total variable cost is $2,500.
Therefore, the zero-profit point is $2,750 ($250 fixed costs + $2,500 variable costs).
To determine the price at the zero-profit point, we can use the zero-profit point formula you mentioned. However, since we don't have the price per unit, we need to solve for it using the given information. Here's how you can do it:
1. Start by calculating the total variable cost for each unit produced. Add up the marginal costs for each computer produced:
- Marginal cost of the first computer: $700
- Marginal cost of the second computer: $250
- Marginal cost of the third computer: $300
- Marginal cost of the fourth computer: $350
- Marginal cost of the fifth computer: $400
- Marginal cost of the sixth computer: $450
- Marginal cost of the seventh computer: $500
Total variable cost = $700 + $250 + $300 + $350 + $400 + $450 + $500 = $2,950
2. Next, calculate the break-even quantity, which is the number of units that need to be sold to cover the fixed costs:
Break-even quantity = Fixed costs / Variable cost per unit
Break-even quantity = $250 / $2,950 ≈ 0.0847
Since you can't sell a fraction of a computer, round up to the next whole number:
Break-even quantity = 1
3. Finally, substitute the break-even quantity into the zero-profit point formula to solve for the price per unit:
Price per unit x Number of units = Fixed costs + (Variable costs per unit x Number of units)
Price per unit x 1 = $250 + ($2,950 x 1)
Price per unit = $250 + $2,950
Price per unit = $3,200
Therefore, at the zero-profit point, the price per unit should be set at $3,200.
To determine the price at the zero-profit point, we can use the formula you mentioned:
Price per unit x number of units = Fixed costs + (variable costs per unit x number of units)
In this case, we don't have the price per unit, but we can calculate it by analyzing the variable costs for each unit:
For the first computer: Marginal cost = $700
For the second computer: Marginal cost = $250
For the third computer: Marginal cost = $300
For the fourth computer: Marginal cost = $350
For the fifth computer: Marginal cost = $400
For the sixth computer: Marginal cost = $450
For the seventh computer: Marginal cost = $500
Since the fixed costs are $250, we can subtract this from the total variable costs to find the total cost for each unit:
Total variable cost for the first computer = $700
Total variable cost for the second computer = $250
Total variable cost for the third computer = $300
Total variable cost for the fourth computer = $350
Total variable cost for the fifth computer = $400
Total variable cost for the sixth computer = $450
Total variable cost for the seventh computer = $500
Now we can calculate the price per unit using the zero-profit point formula:
Price per unit x number of units = Fixed costs + (Variable costs per unit x number of units)
To find the zero-profit point, we need to set the left side of the equation equal to the right side:
Price per unit x number of units = $250 + (Total variable cost per unit x number of units)
Since we want to find the price per unit (P) at the zero-profit point, we can rearrange the equation as follows:
Price per unit = ($250 + Total variable cost per unit) / number of units
Substituting the values we calculated earlier:
Price per unit = ($250 + $700) / 1
Price per unit = $950 / 1
Price per unit = $950
Therefore, the zero-profit point price per unit is $950.