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

Popular posts from this blog

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...

What gift did Della buy for Jim and why in "The Gift of the Magi" by O. Henry?

Della buys Jim a watch fob because his watch is his most prized possession. Della and Jim Young do not have much money. Despite this, Della really wants to buy Jim a good Christmas present. She is even willing to sell her hair to get him a nice gift. This is ironic because we learn Della and Jim both highly prize her hair. Now, there were two possessions of the James Dillingham Youngs in which... Della buys Jim a watch fob because his watch is his most prized possession. Della and Jim Young do not have much money. Despite this, Della really wants to buy Jim a good Christmas present. She is even willing to sell her hair to get him a nice gift. This is ironic because we learn Della and Jim both highly prize her hair. Now, there were two possessions of the James Dillingham Youngs in which they both took a mighty pride. One was Jim's gold watch that had been his father's and his grandfather's. The other was Della's hair.  Della is still willing to sell her hair so she can b...

Explain and discuss how the definitions of freedom change for the nation, for the freedmen and for southern whites after the Civil War.

After the Civil War, the definition of freedom changed in the nation, as slavery was ended with the 13th Amendment to the Constitution in 1865. The practice of slavery was disallowed, but definition of the freedom that would take its place was a subject of controversy, ongoing debate, and even violence in the decades to come.  For freedmen, freedom often meant reconciling with their families, who were broken up by slavery; choosing which church to... After the Civil War, the definition of freedom changed in the nation, as slavery was ended with the 13th Amendment to the Constitution in 1865. The practice of slavery was disallowed, but definition of the freedom that would take its place was a subject of controversy, ongoing debate, and even violence in the decades to come.  For freedmen, freedom often meant reconciling with their families, who were broken up by slavery; choosing which church to belong to without being ordered to attend religious services (or not to attend) by their mast...