Question

4. A firm produces computers with two factors of production: labor L and capital K. It's pro- duction function is . Suppose the factor prices are wl = 10 and wK = 100. (a) Graph the isoquants for y equal to 1.2, and 3. Does this technology show increasing, constant, or decreasing returns to scale? Why? (b) Derive the conditional factor demands. (c) Derive the long-run cost function C(y). (d) If the firm wants to produce one computer, how many units of labor and how many units of capital should it use? How much will it cost? What if the firm wants to produce two computers? (e) Derive the firm's long-run average cost function AC(y) and long-run marginal cost func- tion MC(y). Graph AC(y) and MC(y). (1) Label the firm's long-run supply curve on the graph.

Answer 1

Answer:- (4) y = LK 10 , we=10, wp=100 7 for y= 1,2 and 3. y=1) LK = 10:=10 y =99) LK=20 > L=20 y = 37) LK= 30 31 LK 10/2 elő a la tlo owf oo à F 2 3 4 5 6 8 10 10, 192 Y=LK/0) (17) = (121K) = A 2 K/= ypy xo so, this production function exhibits increasing returns to scale KIRS). as, inputs get doubles then output is . more than double also the power of x is greater than 1. ② MRTS = MPL = (& optimality Condition EMPTS (K = & a (K = 0 h)

% 167 km = 6 % 37 =R WK 10 ) © long run cast function : ceg) = Welt Wp K A s we choosing g'+ cupe couverte y ? Fay)= 2w1 (loco @ if firm wants to produce y = 1 units 1 t A x 22 y=+ = "=(100)% = 10 units of labour Ks (10)l2 = unit of freedom - Capital for y=1 = (L=10, K=1) for y=2> (2=14 **/* = 1:41)