Question

Intermediate macroeconomic theory I (ECON303) Tutorial #3: The firm's problem Paul owns a firm that produces output (Y) with capital (K) and labour (N) accord- ing Y = zk" N i n which z is total factor productivity. Say that z = 100, that K = 1. and that a = 0.5. Each worker supplies one unit of labour. Each unit of labour is paid the wage rate w. The price at which output is sold is P = 1. Suppose that w = 6.25 in the labour market. a) When Paul hires 16 workers, each worker produces 25 goods on average (that is, Y/N = 25). If he hires 9 more workers, then Y/N falls to 20. Has Paul hired lazy workers? Explain. Explain how Paul can make each worker more productive. b) Paul observes the wage rate and then decides to hire 100 workers (i.e. to set N = 100). Is Paul a good businessman? Explain. How many workers should Paul hire? c) The government decides to prevent any firm from polluting. Paul discovers that polluting can be avoided at the cost of 0.25 units of output per unit of output produced. How many workers will Paul hire if w = 6.25? d) To alleviate the cost of reducing pollution, the government decides to pay Paul's firm 1.25 per worker hired. How many workers will Paul hire if w = 6.25? e) How will the policies introduced in c) and in d) affect the firms inverse labour demand curve? How will the equilibrium wage be affected if all firms in the economy are identical to Paul's firm? Illustrate with a graph.

Please be specific in your answers. Thanks a lot!

Answer 1

Solution in To solve the Given that The production function is given by y = Akan when z=100 K= 1 and a=0.5 the production function is given by - Y= 10o No5 when N=16 then Y= 100 (1680-5 - 400 When Ñ - 4025 N=25 then Y= 100 (2500.5 - - 500 * - 500-20 25 Thus it is observed that with me in labour hired from 16 to 25 the average Scanned wproductivity declined from 25 to 20. CamScanner CsScanned produs

Il is because of dimin nishing marginal producturity of labour, given capital & technology is given as constant. fach product can be made productive by increasing deployment of capital investment of using improved technology of production (b) the wage is given by w = 6.25 the price of each product - YESP=1 when N= loo, the value of output y produced is P = Ploo No.5 1X100 (100)05 - 1000 The total cost incurred as WN = 6-25 X 100 = 625 the total profit is: 375 Scanned with CamScanner

paul is not a good business man because at the time of deciding for number of workers to be hired he should have profit maximizing objective in his mind for profit maximization, value of the Marginal product of the labour should be equal to marginal cost of hiring & unit of - labour the value of the marginal product of the labour VMPN is given by NMPN = PX MPN The marginal product of the labour MPN is given by MIP = Oy ON -50 N 0.5 Given pal value of the marginal product of the labour VMPN Equasto UMPN = PX MPN = 1X50 nog - 50 woor Scanned with CamScanner

it shall be noted that the marginal cost of hiring I labour is w = MCN = 6.25 Hence as per profil- maximizing condition VAMPN = MEN 50 Nog 625 N264 the profit is Profit - TR-TC - PY-WN - 1x100 (6455 24X625 - HOO thus pack should have hired 64 workers instead of loo workers and with this he Could have earned not profil- of Hoo instead of only 375 - (6) In presene of avoidance of pollution at the cost of 0.25 per unit of output produced, The profit is given by profit = TR-TG - PY - WN -0.254 - 1 X 100 (N) 2 6.25 N - 0-257 Scanned with - 1X100 (n) 0:5 - 6.25 -6-25 Xloc 9 5 CamScanner

-8.75 Y - 6.25N = 75 (N) 8.5 6.25 N thus for profit maximization Profit ON :o 3705 No.5 6.25=0 N=36 thus paul should have 36 workers it W = 6.25 and when paul need to incor the cost of 0.95 per unit of output produced to avoid pollution (d) when Government pays paul- 1.25 per worker hired to alleviate the cost & reducing pollution then profit is given by profit = TR-TC = P + 1.25 N-AN = 1X100 (170971-25 N-6.95 N - 1 X 100 (N)055N Thus, for profit maximization aprofit so ONO 56 No 3.5=0 - N=loo chus paul would hive 100 workers ist w = 6.25 and when government pays pool 1.25 per workey hired CamScariben alleviate the cost of reducing polletion. L