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Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives exactly 3,715,000.

Please don't say that right answers are wrong when you are unable to replicate them on your own. It causes those who don't know any better to downvote.

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives exactly 3,715,000.

Please don't say that right answers are wrong. It causes those who don't know any better to downvote.

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives exactly 3,715,000.

Please don't say that right answers are wrong when you are unable to replicate them on your own. It causes those who don't know any better to downvote.

3 added 114 characters in body
source | link

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives exactly 3,715,000.

Please don't say that right answers are wrong. It causes those who don't know any better to downvote.

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives 3,715,000.

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives exactly 3,715,000.

Please don't say that right answers are wrong. It causes those who don't know any better to downvote.

2 added 424 characters in body
source | link

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives 3,715,000.

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

Note the revenue is the quantity sold in each country times its respective price. Write out the profit equation $$ \pi= Q_a*P_a+Q_b*P_b - TC(Q_a+Q_b) $$ You already have expressions for $P_a$ and $P_b$ in terms of $Q_a$ and $Q_b$. Substitute these in. The result will be a profit function in terms of only $Q_a$ and $Q_b$. This is your profit function.

Take the derivative of the profit function with respect to $Q_a$. Set equal to 0 and solve for $Q_a$. Repeat for $Q_b$.

If you do it right, you will get $Q_a=450$ and $Q_b=4750$. Substitute these into the profit equation to get the total profit.

All these types of questions are solved the same way.

  1. Write out the correct profit function.

  2. Substitute everything in until the only remaining variables are the things you are able to control (in this case, the quantities).

  3. Take derivatives with respect to each choice variable and solve the resulting first order conditions (which sometimes may be a system of equations, but not here).

  4. Substitute your optimal quantities back in to get the resulting profit.

  5. In a more complex case you should also take the second derivative to ensure that you are getting the maximums, not the minimums.

=================== EDIT: Additional Help =============

Profit function:

$$ \pi=1000Q_a - Q_a^2+2000Q_b-0.2Q_b^2-100(Q_a+Q_b)-1000000 $$

First order conditions $$ \frac{d\pi}{dQ_a}=1000-2Q_a - 100 $$ $$ \frac{d\pi}{dQ_b}=2000-0.4Q_b - 100 $$

Note that from the second first order equation $$ Q_b=\frac{2000-100}{0.4} = 4750 $$

Substituting 450 and 4750 into the profit function gives 3,715,000.

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