Skip to main content

If a firm faces the marginal cost schedule MC = 180 + 0.3 q^2 and the marginal revenue schedule is MR = 540 – 0.6 q^2 and total fixed cost is Rs....

First, we need to figure out what the profit-maximizing quantity sold would be, given these demand and supply schedules.For that, set marginal revenue equal to marginal cost:


MC = 180 + 0.3 q^2 = MR = 540 – 0.6 q^2


0.9 q^2 = 720q^2 = 800


q = 20 sqrt(2) = 28.28


Now we need to figure out what the total revenue and total cost would be.That means we need to integrate ...

First, we need to figure out what the profit-maximizing quantity sold would be, given these demand and supply schedules.

For that, set marginal revenue equal to marginal cost:


MC = 180 + 0.3 q^2 = MR = 540 – 0.6 q^2


0.9 q^2 = 720
q^2 = 800


q = 20 sqrt(2) = 28.28


Now we need to figure out what the total revenue and total cost would be.

That means we need to integrate both of these marginal functions, and then find the appropriate initial condition to set the constants.

TR = int MR dq = int 540 - 0.6 q^2 dq = 540 q - 0.2 q^3 + C
What is the constant? Well, if we sell zero things, we should get zero revenue. So C = 0.

TR = 540 q - 0.2 q^3

TC = int MC dq = int 180 + 0.3 q^2 dq = 180q + 0.1 q^3 + D
If we sell zero things, is our cost zero? No. We still pay our fixed cost. We're told that our fixed cost is in fact Rs 65. So D = 65.

TC = 180 q + 0.1 q^3 + 65

Now all we have to do is subtract these two to get profit, and then substitute in the profit-maximizing quantity we found earlier:

TP = TR - TC = 540 q - 0.2 q^3 - (180 q + 0.1 q^3 + 65)
TP = 360 q - 0.3 q^3 - 65
TP = 360 (20 sqrt(2)) - 0.3 (20 sqrt(2))^3 - 65
TP = 7,200 sqrt(2) - 4,800 sqrt(2) - 65
TP = 2,400 sqrt(2) - 65 = 3,329.11

Thus, if they properly maximize profit, their profit will be Rs 3,329.11.

Comments

Post a Comment

Popular posts from this blog

Can you analyze the poem "Absolution" by Siegfried Sassoon?

Sure! Siegfried Sassoon fought in World War I and was wounded in battle; he spent much of his life speaking out against war, and these pacifist feelings are easy to see in his poems. This one, "Absolution," was published in 1917, the same year that Sassoon was hospitalized for what we know today as post-traumatic stress disorder. "Absolution" is a short poem that contains three stanzas of four lines each. The word "absolution" means "forgiveness," and... Sure! Siegfried Sassoon fought in World War I and was wounded in battle; he spent much of his life speaking out against war, and these pacifist feelings are easy to see in his poems. This one, "Absolution," was published in 1917, the same year that Sassoon was hospitalized for what we know today as post-traumatic stress disorder. "Absolution" is a short poem that contains three stanzas of four lines each. The word "absolution" means "forgiveness," and the v...
Post a Comment
Read more

How and why does James Gatz become Jay Gatsby? Describe the young Gatsby/Gatz.

James Gatz, a poor Midwestern boy of probable Jewish lineage, becomes Jay Gatsby, a presumed WASP and wealthy socialite, when he moves to New York City and acquires his fortune. It is wealth that has allowed Gatz to transform himself into Gatsby. However, those who know his background (e.g., Daisy and Tom Buchanan) never allow him to forget that he is nouveau riche -- that is, an upstart who has just recently made his fortune,... James Gatz, a poor Midwestern boy of probable Jewish lineage, becomes Jay Gatsby, a presumed WASP and wealthy socialite, when he moves to New York City and acquires his fortune. It is wealth that has allowed Gatz to transform himself into Gatsby. However, those who know his background (e.g., Daisy and Tom Buchanan) never allow him to forget that he is nouveau riche -- that is, an upstart who has just recently made his fortune, whereas they arose from well-to-do families. Gatz became Gatsby through determination and discipline. At the end of the novel, the narr...
Post a Comment
Read more

In chapter one of The Great Gatsby, what advice does Nick's father give him? How does this make him a good person to tell this story?

Nick says that his father advised him that, before "criticizing anyone," he "remember that all the people in this world haven't had the same advantages" as Nick.  As a result, Nick claims that he is "inclined to reserve all judgments," presenting himself to the reader as a fair and dispassionate arbiter of character, and thus, a reliable narrator.   The problem is that Nick immediately reveals himself as anything but reliable, as he then launches... Nick says that his father advised him that, before "criticizing anyone," he "remember that all the people in this world haven't had the same advantages" as Nick.  As a result, Nick claims that he is "inclined to reserve all judgments," presenting himself to the reader as a fair and dispassionate arbiter of character, and thus, a reliable narrator.   The problem is that Nick immediately reveals himself as anything but reliable, as he then launches into a discussion of how pe...
Post a Comment
Read more