Question

Suppose the production function is given as Q = VLK. Suppose also that the price of labor w = 10 and the price of capital r = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves for labor and capital. 6) Derive the long run total cost function. 7) What is the long run average and marginal cost functions? 8) Calculate the output elasticity of total cost? Based on your calculated elasticity, what is the type of return to scale that the producer faces. 9) Suppose that capital is fixed at a level K . What is the short run total cost function for this production function. 10) What is the short run average variable cost and short run average fixed cost functions?

Answer 1

Q) 1.) 0-40. Page No : Q = NUK , W =10, 95o Quant Q² LK K= 02/L A Q (AL, AK) = 2 2 [2.Al2 kl2 =ANLk exhibits CRS Ang Now MRTS = MPLIMPI = KIL OMRTS /aL = -K/2² <0, 1 80 MRTS is diminishing - 3 9N MPL = 20/0L = 13 J K L AMPL LO 80 Diminishing Marginal Returns OL 5 at Eqm from MRTS=W/8 KIL = 10/40 - 4K = L proda fund Q² = 4 K K >, Q²- 4 K2 K* = Q1a, 13 40/2 = 20 K= (024) 22 6) 7) 8) LRT= COLA +8K* = 5 40(012) + 10 (20) = 200+ 200 = 400 LRT C= 400 LRAC = LRTC|Q = 40, LR MC= ƏLRTC12Q= 40 a InLRTC 1 = opp elasticity Dealna en LRTC= ln 40+ lno olp el of total cost aln LRTC /alno = 1 Ang 9 as olf elasticity = 1, So CRS Q² = LK, 8. then Lc" = 0²/ K So TC= Colch + ok - TC. = wa/k tok a ocuts SR of C= OK S R PUC- we? WQ 01. 06.12 10 Hong