K=4 then q=4.IfL=5 and K=4then q=4.24.If L=6 and K=4 then q=4.47 Marginal product of labor falls from 24 to.23 9-3K2 This function exhibits increasing returns to scale.For example,ifL is 2 and K is 2 then q is 24.If L is 4 and K is 4 then q is 192.When the inputs are doubled, output will more than double.notice also that if we increase each input by the same factor then we get the following q=3L0)2=23LK2=g Since is raised to a power greater than 1,we have increasing retums to scale The marginal product of labor is constant and the marginal product of capital is ne cacth erer o capital is MPK=2*3*L*K.As K increases,MPK will increase.If you do not know calculus then you can fix the value of L,choose a starting value for K,and find q. Now increase K by 1 unit and find the newq.Do this a few more times s and you can calculate marginal product.This was done in part b above,and is done in part d below. d. 9=K This function exhibits constant returns to scale.For example,if L is 2 and K is2 When the inputs are edoubled.ou if we increase each input by the same factor then we get the following: q4=(L)(2K)产=LK= Since A is raised to the power 1,we have constant retumns to scale. The marginal product of labor is decreasing and the marginal product of capital is decreasing.Using calculus,the marginal product of capital is For any given value ofL,as K increases,MPK will increase. Ifyou do not know n you can fix the value of L,ch sta lue for k and find a Let L=for example. If K is 4 then q is 4,if K is 5 then q is 4.47,and ifK is 6 the q is 4.89.The marginal product of the 5th unit ofK is 4.47-4=0.47,and the marginal product of the 6th unit of K is 4.89-4.47=0.42.Hence we have diminishing marginal product of capital.You can do the same thing for the marginal product of labor. e.9=42+4KK=4 then q=4. If L=5 and K=4 then q=4.24. If L=6 and K=4 then q= 4.47. Marginal product of labor falls from 0.24 to 0.23. c.  q = 3LK 2 This function exhibits increasing returns to scale. For example, if L is 2 and K is 2 then q is 24. If L is 4 and K is 4 then q is 192. When the inputs are doubled, output will more than double. Notice also that if we increase each input by the same factor   then we get the following:  q' = 3(L)(K) 2 =  3 3LK2 =  3 q . Since   is raised to a power greater than 1, we have increasing returns to scale. The marginal product of labor is constant and the marginal product of capital is increasing. For any given value of K, when L is increased by 1 unit, q will go up by  3K 2 units, which is a constant number. Using calculus, the marginal product of capital is MPK=2*3*L*K. As K increases, MPK will increase. If you do not know calculus then you can fix the value of L, choose a starting value for K, and find q. Now increase K by 1 unit and find the new q. Do this a few more times and you can calculate marginal product. This was done in part b above, and is done in part d below. d.  q = L 1 2K 1 2 This function exhibits constant returns to scale. For example, if L is 2 and K is 2 then q is 2. If L is 4 and K is 4 then q is 4. When the inputs are doubled, output will exactly double. Notice also that if we increase each input by the same factor   then we get the following:  q' = (L) 1 2 (K) 1 2 = L 1 2K 1 2 = q . Since   is raised to the power 1, we have constant returns to scale. The marginal product of labor is decreasing and the marginal product of capital is decreasing. Using calculus, the marginal product of capital is . For any given value of L, as K increases, MPK will increase. If you do not know calculus then you can fix the value of L, choose a starting value for K, and find q. Let L=4 for example. If K is 4 then q is 4, if K is 5 then q is 4.47, and if K is 6 then q is 4.89. The marginal product of the 5th unit of K is 4.47-4=0.47, and the marginal product of the 6th unit of K is 4.89-4.47=0.42. Hence we have diminishing marginal product of capital. You can do the same thing for the marginal product of labor. e.  q = 4L 1 2 + 4K