Given the following information, answer the following:
TR=$3Q
TC= $1,200 = $2Q
1. what is the break-even level of output?
2. If the firms sells 1,300 units, what are its earnings or losses?
3. If sales rise to 2,000 units, what are the firms earnings or losses?
4. If the total cost equation were TC=$2,000 = $1.80Q, what happens to the break-even level of output units?
To answer these questions, we need to understand some basic economic concepts and use formulas related to break-even analysis.
1. Break-Even Level of Output:
The break-even level of output refers to the quantity at which a company's total revenue (TR) equals its total cost (TC), resulting in zero profit or loss. To find the break-even level of output, we can set TR equal to TC and solve for Q.
Given:
TR = $3Q
TC = $1,200 + $2Q
Setting TR = TC, we have:
$3Q = $1,200 + $2Q
Simplifying the equation:
$3Q - $2Q = $1,200
$Q = $1,200
Therefore, the break-even level of output is Q = 600 units.
2. Earnings or Losses (when selling 1,300 units):
To find the owner's earnings or losses, we can calculate the difference between total revenue and total cost for a given level of output.
Given output (Q) = 1,300 units:
TR = $3Q = $3(1,300) = $3,900
TC = $1,200 + $2Q = $1,200 + $2(1,300) = $1,200 + $2,600 = $3,800
Earnings or losses = TR - TC = $3,900 - $3,800 = $100 (positive indicates earnings, negative indicates losses)
Therefore, when selling 1,300 units, the company has earnings of $100.
3. Earnings or Losses (when sales rise to 2,000 units):
Using the same calculation method as above, we can find the earnings or losses when sales rise to 2,000 units.
Given output (Q) = 2,000 units:
TR = $3Q = $3(2,000) = $6,000
TC = $1,200 + $2Q = $1,200 + $2(2,000) = $1,200 + $4,000 = $5,200
Earnings or losses = TR - TC = $6,000 - $5,200 = $800
Therefore, if sales rise to 2,000 units, the company has earnings of $800.
4. Impact of changing the total cost equation:
If the total cost equation changes to TC = $2,000 + $1.80Q, we need to find the new break-even level of output.
Given:
TR = $3Q
TC = $2,000 + $1.80Q
Setting TR = TC:
$3Q = $2,000 + $1.80Q
Simplifying the equation:
$3Q - $1.80Q = $2,000
$1.20Q = $2,000
Q = $2,000 / $1.20
Q = 1,666.67
So, with the updated total cost equation, the break-even level of output would be approximately Q = 1,666.67 units.