Question

3. Irmas Handicrafts produces plastic deer for lawn ornaments. Its hard work, says Irma, but anything to make a buck. Her production function is given by f(21, 12) = (min-1, 2.c2})"/2, where I is the amount of plastic used, 22 is the amount of labor used, and f(21.12) is the number of deer produced. (a) On a graph, draw a production isoquant representing input combinations that will produce 4 deer. Draw another production isoquant representing input combinations that will produce 5 deer. (b) Does this production function exhibit increasing, decreasing, or constant returns to scale? (c) If Irma faces factor prices (1, 1), what is the cheapest way for her to produce 4 deer? How much does this cost? (d) At the factor prices (1, 1), what is the cheapest way to produce 5 deer? How much does this cost? (e) At the factor prices (1, 1), what's the cost of producing y deer with this technology c(1,1,y)? (f) At the factor prices (W1, wy), what's the cost of producing y deer with this technology cw1, W2,y)? (g) If w1 = wg = 1, what's Irmas marginal cost of producing y units of output MC(y)? What's the number of units of output that she would supply at price p? At these factor prices, what's her average cost per unit of output AC (y)? (h) If the competitive price of the lawn ornaments she sells is p = 48, and wi = w2 = 1, how many will she produce? How much profit will she make? (i) More generally, at factor prices w and w2, what's her marginal cost function MC(W1, 12, y)? At these factor prices and an output price of p, what's the number of units she will choose to supply S(p, w1, w.)?

Answer 1

Figure 1

15- q=5 1024 10 20 30 40 50

3.a) Equation of iso quant: q: (min {z, ?? *2})? For q=1, a: (min {xi, 222}} . :18 • min szi, azy} For 2:6, 5. { min {x, 22233 . .. 25 min{24, 222} . Figure - by] b) Lets increase xe, x2 by constant & 0 .q' = (min {xe 2x 223 B = x/2 (min {xi, 222}}'² a <q ( production function ... exhibit decreasing retwen to scale) 1. c) At equilibrium : x=282 : ::: 4 = (min 8x4,222})? ::24 = 16 :: x2 = 16/2 = 8 c = wie+ W, X = 16+8 = 24 2,4235 d) similarly for 9:5, ady for q=5 2: 25 . ' .. ..x2 = 23:12 :. TC 125+12 = 37.5 q=4 x2 = 9 e) Similarly for ". .. . :! ... yo 942 : . ico. 392/2

f) Similarly for qan, xal2 = y M = "? . ::22; 172 . .:C: wig? + W2772 . :.6: 2w, twy y? g) for W, 3 W, =li;.ca e y2 :. AC(y) = y 2.MC(Y) = 34 At price p the supply is. McCy) =p . . . or, 3y - þ. ..y = P13 1. At this level. Ac(y) = 2 2 1/3 = b h At p= 48, W, W221; y = /3 = 48 = 16 Accy) = 1/2 = 24 ..^(y) = (p-AC) y = 29x16 = 384 . with wi, wz: Moly) = (awit wa) y At equilibrium, Mccy) = h .. or (2w,+ Wz) y =p ： 9：2u+ w, :: 516,wa, wa) * z wa Wz