It is interesting to see how managers often study the profit margin-sales relation over the life cycle of individual products, rather than the more direct profit-sales relation. This is because profit margins are a good indicator of the relative profits that a firm can make from a given product. High profit margins suggest that customers value the product and still want to buy it which is good for a firm while low profit margins suggest the opposite.
Besides this there are some statistical advantages as well. For instance, profit and sales are both related to the size of a firm which may lead to a relation between the size of the firm and the variation in the disturbance term for a given profit-sales relation thereby leading to heteroscedasticity which may limit the accuracy of the required information.
Market demand estimation is possible when all the independent variables can be identified and separated from the dependent variable. It is only then that the estimation of market demand can be done. Otherwise, one can get stuck in what is called as the identification problem. When demand and supply curves keep shifting it becomes difficult to predict their function and thereby almost impossible to estimate the market demand. This problem usually occurs because some of the factors that affect demand also affect supply which may not allow us to identify the two separately.
A. By setting MR=0 and solving for Q, we get the revenue maximizing price-output combination. The calculations are as follows:
Now, calculating MR:
so it is a revenue maximizing model.
Setting this equal to 0, we get the following equation:
Thus, on solving we get Q equal to 35 and further we can calculate P as follows:
Thus, P equals $35.
For this level of P and Q, TR would be the product of the two which equals $1,225 per day.
Now, profits are calculated by subtracting total cost from total revenue. The total cost is Q times the marginal cost which is $30 times 35. On calculating, we see that there is a profit of $175 per day.
B. For calculating the profit maximizing level of output, we set
or MR=MC as shown below:
On further calculation, we get Q as 20 which can be substituted in the equation for P to get P as $50.
so it is a profit maximizing model.
For this level of P and Q, TR would be the product of the two which equals $1,000 per day.
Now, profits are calculated by subtracting total cost from total revenue. The total cost is Q times the marginal cost which is $30 times 20. On calculating, we see that there is a profit of $400 per day.