****HELP PLEASE****
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 the questions, we need to understand the concepts of break-even level of output and total cost.
1. Break-even level of output:
The break-even level of output refers to the point at which a company's total revenue (TR) equals its total costs (TC), resulting in neither a profit nor a loss. Mathematically, it is the quantity (Q) at which TR = TC.
Given the information, we have:
TR = $3Q
TC = $1,200 + $2Q
Now, equate TR and TC to find the break-even level of output:
$3Q = $1,200 + $2Q
Rearrange the equation:
$3Q - $2Q = $1,200
Combine like terms:
$Q = $1,200
Therefore, the break-even level of output is 400 units.
2. Earnings or losses when selling 1,300 units:
To calculate the earnings or losses when selling 1,300 units, we need to compare the total revenue (TR) and total cost (TC) at this level of output.
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
Therefore, the earnings when selling 1,300 units are $100.
3. Earnings or losses when sales rise to 2,000 units:
Using the same method as before, we calculate the earnings or losses when sales rise to 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, the earnings when sales rise to 2,000 units are $800.
4. Changes in the break-even level of output if the total cost equation changes:
If the total cost equation were TC = $2,000 + $1.80Q, the break-even level of output would change.
Let's find the new break-even level of output:
TR = $3Q
TC = $2,000 + $1.80Q
Equating TR and TC:
$3Q = $2,000 + $1.80Q
Rearranging the equation:
$3Q - $1.80Q = $2,000
Combine like terms:
$1.20Q = $2,000
Solving for Q:
Q = $2,000 / $1.20
Q = 1,667 units
Therefore, if the total cost equation changes to TC = $2,000 + $1.80Q, the break-even level of output increases to 1,667 units.