Question

Suppose that a companies production function is given by: f(L;K) = (10K^3L^2)/(L+K)

a) Does this production function exhibit increasing, constant, or decreasing returns to scale? Algebraically justify your answer.

b) If there is a wage of 10 and a rental rate of capital of 1, then find the company's expansion path.

Answer 1

e) FLLIK) = 10K² L² Ltk FCAL, dk) = lorax) 3 (AL) alt dk) 3 lok 3 d2 (2 A[17) 15 Lok??) Ltk = t ( 10k??) | LK d4 ECL, K) = exhibits increasing Theer, production the returns to scale.

6) - E(lik) = 10x3 22 ( 2) MP2 = OF = (L+K) (20k3L)- 10x3,² (170) 22 . Catk) 2 0 - Jok 31 [ 2(2+X) - 2) 1L +x)2 = 10k3L ( 22+2K-L) (2+ x)2 MPL = 10K3L(+2x) (2+ x)2 MPx = DE = (L+K) 130k²L2) - 10k 3, 2 (0+1) (LAK) 10 K 212 [341+k) - K ] (L+k) ² = JOk2L² | 32+ 3k-k). (L+K) 2 = 10K22231+2K) (tk)? MRTS = MIL MPK JOKPL (1721) O JOK?L?32+21) (27K) 2 o 12+x)2

Lok² L (L+2K) & stor (tkot tok ²2² (32Z2x) K.KxLL +2K) xrx.2 (32+2K) KL[+2x) 2 (32 +21) KL+zk² 322 2KL Expansion MRTS path is given by = w K2+QK² 31² 2KL = 10 KL + 262= 30L? +20kh 2x² – 302? + KL- 2o8L 50 2x2 – 3012 - 19XL Co Theer, expansion path is 2K² – 3042 - 19KL 20