For each of the following production functions determine...

For each of the following production functions, determine whether returns to scale are decreasing, constant, or increasing (show your computations). a. Q = 3K + 2L + KL b. Q = 20K^0.7L^0.5 The multiplicative production function in part b is known as: ________________________ production function.

Transcript

00:01 Hello students, we are given a question here determine whether returns to scale are decreasing, constant or increasing.

00:07 So we are given here some functions.

00:09 So we will start with first part.

00:12 So we are given here that the q is equals to 3k plus 2l plus kl.

00:19 So first of all we are supposed to know that here let k and l are increased by lambda proportion.

00:26 Let k and l are increased by, okay, students, increased by lambda proportion.

00:41 So here we can just say that the q of lambda k comma lambda l is equals to three times of lambda k plus two times of lambda l plus.

00:55 Here we can just say that it should be lambda k times lambda l okay students so basically we can say that three lambda k plus two lambda k sorry two lambda l plus lambda square kl so basically we can just say that here when we take lambda as common we will get 3k plus 2 l plus lambda kl okay students so as we are supposed to to know that here it is increased by lambda it means we can say that output increases by increases by more proportion students more proportion so here we can say that increasing returns to scale increasing returns to scale students now we will go to the second part what we are given the function is given as q is equal to 20 times k to the power q is equal to 20 times k to the power 0 .7 and times l to the power 0 .5 so here we can just say that q is equal to put in by putting q of lambda k comma lambda l what we will get it should be 20 times lambda k to the power lambda k whole power is 0 .7 lambda l whole power is 0 .5 so basically we are supposed to know that it is 20 times lambda to the power 0 .7 times k to the power 0 .7 times lambda to the power 0 .5 times l to the power 0 .5 so we can say that the both the powers of lambda will be added so 20 times lambda to the power here we can just say that it should be like lambda to the power point seven plus point five it means 1 .2 and times it should be 20 times k to the power 0 .7 and l to the power 0 .5 okay students so we can just say that there lambda to the power 1 .2 times q so we can say that here output increases by we can say that output increases by okay, students, increases by 1 .2 proportion.

03:32 1 .2 proportion.

03:35 So we can say that it is increasing returns to scale...

Question

For each of the following production functions, determine whether returns to scale are decreasing, constant, or increasing (show your computations). a. Q = 3K + 2L + KL b. Q = 20K^0.7L^0.5 The multiplicative production function in part b is known as: ________________________ production function.

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