Question

Sorry this problem is little long, thank you so much!

8. Consider a firm with a production function Q = Q(L), a total revenue function TR=TR(Q), and total cost function TC = TC(Q).

Answer 1

In Economics, we learn that each firm benefits by deploying policy set approved by their management. The management comes up with the policy depending on their understanding of their business model.

Its be this knowledge that a firm decides to either maximize their profits, or sales or just quantity.

Maximizing profit essentially means -

$\prod = TR - TC$ ,

here  $\prod$ stands for profits.

Therefore profit maximization will occur at a point where the difference between total cost and total revenue is maximum.

We now would use differential calculus to maximize the equation.

The first order condition for maximizing a function is to differentiate the equation and equate it to zero.

This means,

$\Delta TR / \Delta Q - \Delta TC / \Delta Q = 0$

Now since the first order condition also states that-

$\Delta \Pi / \Delta Q = 0$

Therefore,

$\Delta TR / \Delta Q = \Delta TC / \Delta Q$

Now, by definition, change in total revenue due to change in quantity is referred to as Marginal Revenue and change in total cost due to change in quantity is referred to as Marginal Cost.

Therefore, we can say that the first order condition is as follows,

$MR = MC$

This also can be stated as - any firm will maximize its profits at the point where the slope of Total Revenue curve will be equal to the slope of Total cost curve. This is the necessary condition for profit maximization.

The second order condition-

The SOC for profit maximization

dz bp) bp d(TR) d [d(TC) bp dq d d(TC) d <0 dq bp d(TR) bp dq dq d(MR)(MC) 11

Date: / Page No. Revenve TR Cosk Outper Profit Maniguton

The graphical representation states that at point $q_{0}$, although first order condition is being satisfied, it is not the profit maximizing output. However, point $q_{1}$ follows both conditions of profit maximization and is thus the output at which the firm can maximize its profits.

Similarly, you may find the maximizing condition in the similar fashion.

You may write down in the comments section if you are unable to do it on your own.

And for part d, I will shortly be commenting on the comments section due to lack of time availability.

Thanks!