In its first year, Abol buna Company had the following experience.
Sales = 25,000 units Selling price = Birr 100
Total variable cost = Birr 1,500,000 TFC = Birr 350,000
Required:
Develop revenues, cost, and profit functions for the company in terms of quantity.
for x units,
revenue r(x) = 100x
cost c(x) = x*AVC + TFC = 1500000/25000 x = 60x + 350,000
profit p(x) = r(x)-c(x)
To develop revenue, cost, and profit functions for Abol buna Company in terms of quantity, you'll need to use the given information and apply the relevant formulas.
1. Revenue (R):
Revenue is the total sales generated by the company. It can be calculated by multiplying the selling price per unit by the number of units sold.
Formula: R = Selling Price * Quantity
In this case, the selling price per unit is Birr 100 and the quantity is given as 25,000 units.
R = 100 * 25,000
R = Birr 2,500,000
So, the revenue function in terms of quantity is R = 2,500,000Q, where Q represents the quantity.
2. Total variable cost (TVC):
Total variable costs are the costs that vary with the quantity produced or sold. In this case, the total variable cost is given as Birr 1,500,000.
So, the TVC function in terms of quantity is TVC = 1,500,000.
3. Total fixed cost (TFC):
Total fixed costs are the costs that do not vary with the quantity produced or sold. Here, the TFC is given as Birr 350,000.
So, the TFC function in terms of quantity is TFC = 350,000.
4. Total cost (TC):
Total cost is the sum of total variable cost and total fixed cost.
Formula: TC = TVC + TFC
Using the given values:
TC = 1,500,000 + 350,000
TC = Birr 1,850,000
So, the total cost function in terms of quantity is TC = 1,850,000.
5. Profit (P):
Profit is calculated by subtracting total cost from revenue.
Formula: P = R - TC
Using the values calculated above:
P = 2,500,000 - 1,850,000
P = Birr 650,000
So, the profit function in terms of quantity is P = 650,000.
To summarize:
Revenue function (R) in terms of quantity: R = 2,500,000Q
Total variable cost function (TVC) in terms of quantity: TVC = 1,500,000
Total fixed cost function (TFC) in terms of quantity: TFC = 350,000
Total cost function (TC) in terms of quantity: TC = 1,850,000
Profit function (P) in terms of quantity: P = 650,000
To develop revenues, cost, and profit functions for the company in terms of quantity, we need to use the given information. Let's break it down step by step:
1. Revenues: Revenue is calculated by multiplying the quantity sold by the selling price per unit.
Revenue = Quantity Sold * Selling Price
In this case, the selling price is Birr 100 and the quantity sold is given as 25,000 units.
Therefore, the revenue function in terms of quantity (Q) is:
Revenue (Q) = 100Q
2. Variable Costs: Total variable cost (TVC) is given as Birr 1,500,000. To find the variable cost per unit, we need to divide the total variable cost by the quantity sold.
Variable Cost per Unit = Total Variable Cost / Quantity Sold
Variable Cost per Unit = 1,500,000 / 25,000
Variable Cost per Unit = Birr 60
Therefore, the variable cost function in terms of quantity (Q) is:
Variable Cost (Q) = 60Q
3. Total Fixed Costs (TFC): TFC is given as Birr 350,000.
Therefore, the fixed cost function is simply:
Fixed Cost = Birr 350,000
4. Profit: Profit is calculated by subtracting the total cost (fixed cost plus variable cost) from the revenue.
Profit = Revenue - Total Cost
Total Cost = Fixed Cost + Variable Cost
Total Cost (Q) = Birr 350,000 + 60Q
Therefore, the profit function in terms of quantity (Q) is:
Profit (Q) = Revenue (Q) - Total Cost (Q)
= 100Q - (350,000 + 60Q)
= 40Q - 350,000
So, the revenue function is Revenue (Q) = 100Q, the variable cost function is Variable Cost (Q) = 60Q, the fixed cost function is Fixed Cost = Birr 350,000, and the profit function is Profit (Q) = 40Q - 350,000.