00:01
Hello students we are given a question here a firm's long run total cost curve is given as cq is equal to 40 q minus 10 q squared plus q q okay it is actually a small q now here what we are given in the question further over what range of output does the production cost production function exhibit economies of scale over what range of over what range does it exhibit dis -economies of scale and at what quantity is minimum efficient scale so first of all we are supposed to note that here economies economies of scale occurs okay students when marginal cost is greater than sorry marginal cost is less than average cost okay so basically and dis -economies of scales occur when we can write marginal cost is greater than average cost okay and minimum efficient scale occurs scale occurs where marginal cost is equal to average cost is equal to average cost.
01:36
Okay students.
01:38
So basically now we will start our first step.
01:42
So what we are given here, c of q is equal to let's say this is total, we can write it as total cost, okay, which is given as 40 q minus 10 q squared plus q.
01:57
Okay students, we need to find the marginal cost.
02:00
So marginal cost is the derivative of total cost.
02:03
So it will be 40 minus 20 q plus 3 q square okay students and average cost so ac of q a average cost is nothing but the total cost cq divided by number of units it means q so basically when we divide total cost by q what we will get here 40 minus 10 q plus q square okay students now economies of scale economies of scale occurs when mc is less than ac.
02:46
Students, so basically we can say that here, mc is 40 minus 20 q plus 3q square is less than ac.
02:55
It means 40 minus 10 q plus q square.
02:59
As we can see, 40 will be cancelled out by 40.
03:02
As we can say that here, 3q square and minus q square...