A. To maximize profit, the firm should produce at the level of output where MR=MC. In a perfectly competitive market, MR = P = $10.
So, first we need to find the marginal cost (MC) function:
MC = dTC/dq = 10 - 8q + 3q^2
Setting MR = MC:
10 = 10 - 8q + 3q^2
Rearranging and solving for q:
3q^2 - 8q = 0
q(3q - 8) = 0
q = 0 or q = 8/3
Since q cannot be zero (in a competitive market, the firm produces positive output), the firm should produce 8/3 units of output.
B. To find the level of profit at equilibrium, we need to calculate total revenue (TR) and total cost (TC) at the output level of 8/3 units:
TR = Pq = $10 * 8/3 = $26.67
TC = 10q - 4q^2 + q^3 = (10 * 8/3) - (4 * 64/9) + (8/27)
TC = 197.33/27 ≈ $7.32
Profit = TR - TC = $26.67 - $7.32 = $19.35
C. To stay in the market, the firm must cover its variable cost (VC). Variable cost is the part of the total cost that varies with the level of output, i.e. the cost of production excluding fixed costs. In this case, the firm's variable cost is:
VC = 10q - 4q^2 = q(10 - 4q)
The minimum price required to cover VC is the point where VC = P:
q(10 - 4q) = 10
4q^2 - 10q + 10 = 0
Dividing by 2:
2q^2 - 5q + 5 = 0
Using the quadratic formula:
q = (5 ± sqrt(5))/4
Since q cannot be negative (in a competitive market, the firm produces positive output), we take the positive root:
q = (5 + sqrt(5))/4 ≈ 1.56
Therefore, the minimum price required to cover the firm's variable cost is $1.56.
1. Suppose that the firm operates in a perfectly competitive market. The market price of his product is $10. The firm estimates its cost of production with the following cost function
TC=10q-4q2+q3
A. What level of output should the firm produce to maximize its profit.?
B. Determine the level of profit at equilibrium.
C. What minimum price is required by the firm to stay in the market.?
3 answers
The Dean of Students Office of samara University reported that because of strict control over chat smuggling in to the campus, the demand for coffee in swale Café has dramatically increased. How do you justify this report?
There are a few ways to justify this report:
1. Coffee and cigarettes are often seen as complementary goods - that is, goods that tend to be consumed together or have a similar consumer base. If cigarette smuggling is being strictly controlled on campus, it is likely that students who used to smoke cigarettes on campus are now looking for other ways to satisfy their cravings or take a break from studying. Coffee could be a natural substitute for cigarettes in this scenario, leading to an increase in demand for coffee at the Swale Café.
2. It is also possible that the strict control over cigarette smuggling has led to a reduction in smoking overall, leading students who used to take cigarette breaks to now take coffee breaks instead. This would also increase the demand for coffee at the Swale Café.
3. Another possibility is that the strict control over cigarette smuggling has led to a broader cultural shift on campus, with students becoming more health-conscious and looking for ways to improve their well-being. Coffee is often seen as a healthier alternative to smoking, leading more students to choose it as a beverage option. This could also contribute to an increase in demand for coffee at the Swale Café.
Overall, there are several plausible explanations for why the Dean of Students Office at Samara University may have reported an increase in demand for coffee at the Swale Café as a result of strict control over cigarette smuggling.
1. Coffee and cigarettes are often seen as complementary goods - that is, goods that tend to be consumed together or have a similar consumer base. If cigarette smuggling is being strictly controlled on campus, it is likely that students who used to smoke cigarettes on campus are now looking for other ways to satisfy their cravings or take a break from studying. Coffee could be a natural substitute for cigarettes in this scenario, leading to an increase in demand for coffee at the Swale Café.
2. It is also possible that the strict control over cigarette smuggling has led to a reduction in smoking overall, leading students who used to take cigarette breaks to now take coffee breaks instead. This would also increase the demand for coffee at the Swale Café.
3. Another possibility is that the strict control over cigarette smuggling has led to a broader cultural shift on campus, with students becoming more health-conscious and looking for ways to improve their well-being. Coffee is often seen as a healthier alternative to smoking, leading more students to choose it as a beverage option. This could also contribute to an increase in demand for coffee at the Swale Café.
Overall, there are several plausible explanations for why the Dean of Students Office at Samara University may have reported an increase in demand for coffee at the Swale Café as a result of strict control over cigarette smuggling.
3 answers