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

What are some external and internal conflicts that Montag has in Fahrenheit 451?

 Montag, the protagonist of Fahrenheit 451, faces both external and internal conflicts throughout the novel. Some examples of these conflicts are: External Conflicts: Conflict with the society: Montag lives in a society that prohibits books and critical thinking. He faces opposition from the government and the people who enforce this law. Montag struggles to come to terms with the fact that his society is based on censorship and control. Conflict with his wife: Montag's wife, Mildred, is completely absorbed in the shallow and meaningless entertainment provided by the government. Montag's growing dissatisfaction with his marriage adds to his external conflict. Conflict with the fire captain: Montag's superior, Captain Beatty, is the personification of the oppressive regime that Montag is fighting against. Montag's struggle against Beatty represents his external conflict with the government. Internal Conflicts: Conflict with his own beliefs: Montag, at the beginning of th...
Post a Comment
Read more

In A People's History of the United States, why does Howard Zinn feel that Wilson made a flimsy argument for entering World War I?

"War is the health of the state," the radical writer Randolph Bourne said, in the midst of the First World War. Indeed, as the nations of Europe went to war in 1914, the governments flourished, patriotism bloomed, class struggle was stilled, and young men died in frightful numbers on the battlefields-often for a hundred yards of land, a line of trenches. -- Chapter 14, Page 350, A People's History of the United States Howard Zinn outlines his arguments for why World War I was fought in the opening paragraph of Chapter 14 (referenced above). The nationalism that was created by the Great War benefited the elite political and financial leadership of the various countries involved. Socialism, which was gaining momentum in Europe, as was class struggle, took a backseat to mobilizing for war. Zinn believes that World War I was fought for the gain of the industrial capitalists of Europe in a competition for capital and resources. He states that humanity itself was punished by t...
Post a Comment
Read more

Where did Atticus take the light and extension cord in To Kill a Mockingbird?

Atticus brings the light to the courthouse jail so that he can protect Tom Robinson.  Atticus learns that Tom Robinson, his client, is in danger.  A group of white men want to prevent the trial and lynch Robinson. He is warned by a small group of men that appear at his house.  He refuses to back down.  Atticus knows that the Cunninghams will target his client, so he plans to sit up all night with... Atticus brings the light to the courthouse jail so that he can protect Tom Robinson.  Atticus learns that Tom Robinson, his client, is in danger.  A group of white men want to prevent the trial and lynch Robinson. He is warned by a small group of men that appear at his house.  He refuses to back down.  Atticus knows that the Cunninghams will target his client, so he plans to sit up all night with Jim if that’s what it takes to protect him.  Atticus tells the men that he will make sure his client gets his fair shake at the law.  “Link, that boy might go to the chair, but he’s not going till ...
Post a Comment
Read more