Question

Given the following long run production and cost functions: 4 = 1/3K2 C = 15L + 3K (A) What input has diminishing marginal returns? (B) Does this production function display increasing, decreasing or constant returns to scale? (C) What is this firm's expansion path assuming input prices do not change? HTML Editora

Answer 1

9= 13K ( 33 x ² (A) Jq - -2 3 IL 3 k 11 th 2 Ja K 2 TL 31 2 mp = marginal Product of Labor ml k² 2 3 (L) 1 as Labor increases mh decreases, Labor in put has diminish ishing marginal Returns. mp of dk as capital (k) increases mp of capital deur increases de 2KL capital onry Labor in Put has diminis ninishing marginal Returns.

(B) - اب 2 9 = 1 T F (K, L) tol scaling and k by 1 2 F (KIL) = L 3 K - 3 FIR, EL ) = (tl) (tki? 2 2 (t)}, 3 Lotok +2 2 (t ) 3 - K 3 F(tk, tL) (t) F(KIL) F(tk, tel = (t & F(x, 4) with xxl twice So scalling factor of Production for exam pie gives more than twice of output Por Production function disley increasing returns To Scale.

2 q = L k mp = مایه نے 1 3 K MPK cul- 2 LOK & marginal product of Labor & marginal Product of Capital mPx g 2 Cain El cot where w= Price of 2 = ) 3 ILK 3 2 2L K Labor 15 15 3 WIN = ) 2 Ya col- 3 2L K - Price of capital 5 5 => w - 10,5 K 10 L 3 k 3. -> 2 3 cul- K 301K 1 2 2 K 3 = 30L ol k expansion Path = ) K = 30 L