00:01
So for the monopolistically competitive firm, here we have our demand equation given as q equals 36 minus 4b and we have our cost equation as cq as 124 minus 16 q plus q square and we have marginal cost also given in the question as minus 16 plus 2 q and we have to find the inverse demand function for the firm's product profit maximizing level of production and the forms profit so we'll go ahead and solve this step by step so first of all we'll go ahead and find the inverse demand function now what is an demand function inverse demand function this is the part a of our question so inverse demand function reviews or views rise as a function of quantity demanded so solving this so here we have q equals 36 minus 4p.
02:01
Now this comes up as 4p equals 36 minus q.
02:07
So p equals 36 upon 4 minus q upon 4 and p equals 9 minus q upon 4.
02:20
And this is the inverse demand function or the demand function in which price is the dependent variable while quantity is the independent variable.
02:35
Now moving ahead, we have to find the profit maximizing level of production.
02:44
So we know at this is part b of our question.
02:50
And profit maximizing level of production marginal revenue equals marginal cost so first of all in order to find the profit maximizing level of production we have to find the marginal revenue and marginal cost marginal cost is given in the question so we have to find the marginal revenue revenue so first of all will find the total revenue that is tr equals price times output and we have price given as 9 minus q upon 4 times output this comes up as 9 q minus q square upon 4 so marginal revenue will be the first order differentiation of total revenue with respect to output so solving this and we know the formula for differentiation that is differentiation of x to the power n will be nx to the power n minus 1.
04:50
So this comes up as 9 minus q upon 2.
04:56
Let me write this once again.
04:59
So marginal revenue is equal to 9 minus q upon 2.
05:05
This is our marginal revenue.
05:10
And marginal cost is given in the question as minus 16 plus 2q.
05:20
So we will go ahead and equate the marginal revenue equals marginal cost in order to find the profit maximizing level of production.
05:33
So 9 minus q upon 2 will be equal to minus 16 plus 2q.
05:42
So solving this, we have 9...