<p>How do you solve this question?</p>

<blockquote>
  <p>A company has 3 products. They contribute to 30%, 30% and 40% of sales
  respectively.</p>
  
  <p>They have profit margins of 15%, 30%, and 50% respectively.</p>
  
  <p>If the client raises prices by 10% for Product A (assuming costs
  remain constant), what is the change in the company's total gross
  profit?</p>
</blockquote>

<p>Is sales the same as total revenue (TR) or is it the same as profit ($\pi = TR - TC$)?</p>

<p>If it's the same as total revenue, I know that product A contributes 30% to the total sales, i.e.</p>

<p>$$
0.3 \cdot TR = TR_A
$$</p>

<p>Profit margin is given as $\tfrac{TR - TC}{TR}$, and if the profit margin of profit A is 10% then
$$
\frac{1.1 \cdot TR - TC}{1.1 \cdot TR} = 1 - \frac{TC}{1.1 \cdot TR}
$$</p>

<p>If the client raises prices by 10% for product A, the total revenue (TR) is now
$$
TR' = 1.1 \cdot P \cdot Q = 1.1 \cdot TR
$$</p>

<p>But how do i summarize? How can I conclude what the change in company's total gross profit is?</p>

CC BY-SA 3.0
2016-05-25T12:44:05.943Z
Are you assuming that the demand for products is fairly inelastic. That is number of units sold for each product will be same even after price increase ?
Sub-Optimal
CC BY-SA 3.0
2016-05-25T12:46:21.663Z
All else (costs, units of each product sold and costs of each product ) constant, the profit of company will increase by 5.78%.
Sub-Optimal
CC BY-SA 3.0
2016-05-26T15:47:05.137Z
Yes everything is held constant. How did you calculate this?
Jamgreen
CC BY-SA 3.0
2016-05-27T05:09:53.357Z
Just take any example. Calculate the profits and the percentage change.
Sub-Optimal
CC BY-SA 3.0
2016-05-29T07:39:26.843Z
I get a result of 12%. Can you elaborate how you did?
Jamgreen
<cost><profits><price>
Find change in gross profit after price change
Jamgreen
# Find change in gross profit after price change

(Asked by: username_0 on 2016-05-25)

How do you solve this question?

> A company has 3 products. They contribute to 30%, 30% and 40% of sales
> respectively.
>
> They have profit margins of 15%, 30%, and 50% respectively.
>
> If the client raises prices by 10% for Product A (assuming costs
> remain constant), what is the change in the company's total gross
> profit?

Is sales the same as total revenue (TR) or is it the same as profit ($\pi = TR - TC$)?

If it's the same as total revenue, I know that product A contributes 30% to the total sales, i.e.

$$
0.3 \cdot TR = TR\_A
$$

Profit margin is given as $\tfrac{TR - TC}{TR}$, and if the profit margin of profit A is 10% then
$$
\frac{1.1 \cdot TR - TC}{1.1 \cdot TR} = 1 - \frac{TC}{1.1 \cdot TR}
$$

If the client raises prices by 10% for product A, the total revenue (TR) is now
$$
TR' = 1.1 \cdot P \cdot Q = 1.1 \cdot TR
$$

But how do i summarize? How can I conclude what the change in company's total gross profit is?

**Tags:** cost, profits, price

> **Comments:**
> **username_1**: Are you assuming that the demand for products is fairly inelastic. That is number of units sold for each product will be same even after price increase ?  
> **username_1**: All else (costs, units of each product sold and costs of each product ) constant, the profit of company will increase by 5.78%.  
> **username_0**: Yes everything is held constant. How did you calculate this?  
> **username_1**: Just take any example. Calculate the profits and the percentage change.  
> **username_0**: I get a result of 12%. Can you elaborate how you did?  

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## 0 answers

