Question

Example • Market demand Q = 4000-20P • All firms have access to production function q = L^0.25 K^0.25 w=r= 1 originally, but government considering minimum wage increase to w =16. Firms also have fixed costs of 800. • What is the effect on total workers employed? • What is the effect on total firms in the market? • What is the effect on consumers and consumer surplus? P = MC=AC MPK W

Answer 1

Example All times have access to production functions al q=2 0.25k ons Now, marginal product of labor! MPL = da o 0.25_-0175x0.25 and marginal product of Capital: MPK - 0.25L0:25 %-0.75 Now, initially w=8=1 and fined cost is 800 Hnce Total cost equation e= fet whtok where fes fined cost. = 800 Now c= 8004 WLtok = 800+ Ltk Now optimal is put in g condition est MPL - MPL 40.25 1 MPK =) 0.25L-0.75 K 0.25 ÖRS 20.25 k-0.75 - ī 1 => KPL production function wx gut! Now substituting k=2 in the 2= 20.25 k 0.25 0.25 hence a) 2 = 20.25 2 q = Lois Now as K =2 => q2 = L - K=q2 Scanned with CamScanner

Now, substituting L=qz and k=qz in cost huction we qut! c=800+q2tq2 sjes 2927800 Now, marginal cost mc = de = 42 and average cost Ac - 2q²+800 29+ 800 = Now profit in animising condition will be P= MC = AC Now, MC= AC ocems whene 42 = 22 + 800 =) 2q = 800 = 2q = 800 a =) = 20 Ance Mc = 4q = (4*20) = 80 Hace P= mc = 80 Now We know optimal workas hired L=q² = (20)² - 400 K= 400 hence and as L=k Hunce each time will produce q=2o.25 KORS substituting L= 400 and K= 400, we get! q= (400 20:25 1400) 0:25 = 20 wits cs Scanned with CamScanner

and total ettent market demand Q = 400 - 202 =) Q = 4000-(20x80) [substituting P= 807 a) Q = 2400 Hence to stal demand is 2 400 and each tim produces 0 mits, & hence to stal firms in the market - 2400 = 120 2 20 Now, Q = 4000 20p When Pro -> Q = 4 ore when Q 20 => 4000-20p =0 p=200 $80 and quantity Q=2400. Now, equilibrum puce is 200 4000 RA Demand Scanned with CamScanner 2400

Now, consman supls is area of A ABC = £x basc X height -Źx (24000) X (20-80) = 144600 Now, when, minium wage in creash to w = 16. then optimal in put mix condition is: MPL a MPK .) 0.25%-0175 (0.25 0:25 10:25 (-0.75 = 1 -) = 16 => K162 substituting k=16L is the production fraction we gets 9= 20.25 x 0.25 Now - q = 20.25 1162.70.25 =) qe & 40.5 a) (2 2 2 2 ² = 2 4 q=L As k=16L = 16 X 2 = 422 cost function will be 1. e=800t 16 Lt K substifuting vales of kand L we get' Now we dit : cs Scanned with CamScanner

4 e=800t 16 22 7 4 22 =) (= 800+ 4q2 +4q2 =) ( = 80078q2 Now marginal cost me = do = 162 and awuage cost AC = e = 800tsh Now, profit manimising condition ist P= MC=AC Now Mc = At otta 80 +8q 164 = 800 + 82 89= 800 2 892=800 a) q2 = 100 => 9-10 Now, t as P = MC= AC Now when q=10, MC = 169 = (16*10) = 160 hence p= mc= 160 Now when q=10, L= q - Ho (10)^2 25 and K= 4q² = 4X200 = 400 Now, each fim will produce 2= 10:25 +0.25 2/2 = (25) 0-25 1400 20.75 = 10 CS CamScanner Scanned with

and total market demand will be . Q = 4000- 20p a) Q = 4o0o- (20x 160) Hace to ful demand is 800 and each firm produces lomits. Hunce rembu of tims will be 800 g To Now, deased e equilibuon Pice is $160 and quantity is 800 np A 200 I LOD Demand - Q goo 4 000 Consren smpes is = Area of A ABC = £x bune x height = { x (800-0) * (200-160) = 16000 bluce due to inmeasc in mininen wage brow wel to w=16 ne tokial workas employed balls rron 400 to

25 to tel firms in the market de clines from 120 to 8 tims and consumen will pay a higher puce puce increases from $80 to $160 and quantity aclims from 2400 wits to 800 uits and consues emples declines from 144000 to 16000. as puce increa Scanned with CamScanner