i have tried so hard to understand this and i am totally confused. I just don't know where to begin. Can someone please, please help me??
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?
I understand that you are having trouble understanding the given information and need some help. I'll do my best to explain how to find the answers to each question.
1. To find the break-even level of output, we need to determine the level of output at which total revenue (TR) equals total cost (TC). In this case, TR is given as $3Q and TC is given as $1,200 + $2Q. To find the break-even level of output, we equate TR and TC and solve for Q:
TR = TC
$3Q = $1,200 + $2Q
To solve for Q, we can subtract $2Q from both sides:
$3Q - $2Q = $1,200
Simplifying the equation gives us:
$Q = $1,200
Therefore, the break-even level of output is 1,200 units.
2. To find the earnings or losses when the firm sells 1,300 units, we need to calculate the difference between total revenue and total cost at that level of output. We can use the given TR and TC equations to find these values:
TR = $3Q
TC = $1,200 + $2Q
Substitute Q = 1,300 into both equations:
TR = $3(1,300) = $3,900
TC = $1,200 + $2(1,300) = $1,200 + $2,600 = $3,800
To calculate the earnings or losses, subtract TC from TR:
Earnings / Losses = TR - TC
Earnings / Losses = $3,900 - $3,800 = $100
Therefore, the firm's earnings or losses when selling 1,300 units are $100.
3. To find the firm's earnings or losses when sales rise to 2,000 units, we can follow a similar process as in question 2. Substitute Q = 2,000 into the TR and TC equations:
TR = $3Q
TC = $1,200 + $2Q
TR = $3(2,000) = $6,000
TC = $1,200 + $2(2,000) = $1,200 + $4,000 = $5,200
Earnings / Losses = TR - TC
Earnings / Losses = $6,000 - $5,200 = $800
Therefore, the firm's earnings or losses when sales rise to 2,000 units are $800.
4. If the total cost equation were TC = $2,000 + $1.80Q, instead of TC = $1,200 + $2Q, we need to determine how the break-even level of output units would change.
By setting TR equal to TC and solving for Q, we would have:
TR = TC
$3Q = $2,000 + $1.80Q
To solve for Q, subtract $1.80Q from both sides:
$3Q - $1.80Q = $2,000
Simplifying the equation gives us:
$1.20Q = $2,000
Divide both sides by $1.20 to solve for Q:
Q = $2,000 / $1.20
Therefore, the break-even level of output units would change to approximately 1,667 units if the total cost equation were TC = $2,000 + $1.80Q.
I hope this explanation helps clarify the steps and concepts involved in solving these questions. If you have any further questions, please feel free to ask.