Question

Only question b and f need aid

Question B1 Where x is an output produced using inputs labour (l) and capital (k) a) Do the following production functions exhibit decreasing, constant, or increasing returns to scale? Explain your answers (2 marks each) - x = 5070.3k0.3 x = 2020.45 k0.55 x = 570.610k0.6 Suppose our price-taking and wage-taking firm can produce a single output x using inputs labour (l) and capital (k) according to the production function: x = f(1,k) = 8020.5k 0.3 Assume the we operate in a short-run environment where capital is fixed at 100 units: b) Sketch the firm's short-run production frontier, clearly indicating the feasible set of production plans. (3 marks) The market wage paid to labour (w) is £100 per unit of labour employed, and the price the firm receives for each unit of its output (p) is £9. c) If the firm is maximising its profit in the short-term, how much labour (1) does the firm employ (labour is divisible)? (6 marks) d) What is the firm's profit maximising output at this level of labour (where output is divisible)? (4 marks) e) How much profit (Tt) does the firm make in the short-run? (4 marks) f) Moving to the long-run where the firm can also vary the amount of capital it employs. Assuming that the firm must pay a rent (r) of 500 for each unit of capital it employs (but all other prices and factor-prices remain the same), would the firm employ more or less than the 100 units of capital it employed in the short-run? Use any appropriate method to support your answer. (3 marks)

Answer 1

The return to scale from the following production can be find out by the testing of degnee of homogenity. functim. C) R = 5003703 multiply a constant factor in the production function to each Voniable. x = 50 (L) a3 a4.3 50 ,0.30.3 0.3 4.3 then facton out the &. = 0.34 0.3 50 2013 Hora 6.50L-303 = obx so here the degree of homogenity is of which is ress. then one so this production function Follonds decreasing return to scate. 0 , 20 019S K S Multiply the constant factor & to each vewable x = 20 (62) ous cowo.ss. - 2080.45ous poiss, poiss then factor not the & for us tooss 20.45 0.55 - 0' 20 Lous nos follos hence this enoduction function to scate as the value of the dege constant metuan ty is one.

- n=510.6 10korb multiply the constant forton & x = 5(PL) 16 10 CYKJob - 88.668.668.6 1640.6 = 48.64016 5Lood 10 kub = plan CON the as nits production fornetin degnee of homogenety Follows increasing refers to seate in greater then one.

b) given the production function x = 80 L^0.5K^0.3 and capital is fixed at 100 unit then when we increase the number of labour then the production function give the following result

50 סל 100 2252,034 100 2466.98 100 2664,643 100 2848.623 100 3021421 100 3184.857 סט 100

when we plot the data it will show the below figure

A cutput growth productline. 50 60 To sobo 10o