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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?

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  • $\begingroup$ 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 ? $\endgroup$ – Sub-Optimal May 25 '16 at 12:44
  • $\begingroup$ All else (costs, units of each product sold and costs of each product ) constant, the profit of company will increase by 5.78%. $\endgroup$ – Sub-Optimal May 25 '16 at 12:46
  • $\begingroup$ Yes everything is held constant. How did you calculate this? $\endgroup$ – Jamgreen May 26 '16 at 15:47
  • $\begingroup$ Just take any example. Calculate the profits and the percentage change. $\endgroup$ – Sub-Optimal May 27 '16 at 5:09
  • $\begingroup$ I get a result of 12%. Can you elaborate how you did? $\endgroup$ – Jamgreen May 29 '16 at 7:39

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