Question

Problem 1: Isoquant, Isocost Cost Minimizing Approach to Factor Selection: Suppose that as part of the UNCCCC Paris Agreement Green New Deal Plan to rapidly reduce Greenhouse Gas Emissions (GHGs) and other local air pollutants, suppose the elected City Council of the City of K'jipuktuk (Halifax) puts into place a low GHG transport system. As part of the plan, K'jipuktuk Transit, has been electrifying and increasing the size of the city's Public Transit System. So, far to this end, suppose they have ordered 135 new electric buses (e-buses) from the Nova Scotia Electric Bus Company (NSEBC) to be used in the Greater K jipuktuk-Halifax Area. LetQ represent the quantity of these electric buses. NSEBC receives the order and needs to decide how many human hours of labour (L) [in hours/month] and robots (K) [in hours/month] to allocate to make the quantity (Q) e-buses over a one-month period. In addition to L and K, other exogenous factor inputs include, natural capital, human capital, technological factor progress (TFP) level, and manufactured inputs including, electricity, steel, glass, fabrics, etc. These are all assumed to be exogenously captured in the factor labeled "A" in the production function below. Let Q represent the quantity of e-buses made per month according to the following production function. Q(K,L) = A * L2/5 *K3/5. The marginal product of labour and capital are respectively: MP_(K,L) = A* and MPx(K,L) = A* () 25 a) Give one example of each of the following that is relevant to the above context. i) human capital, ii natural capital, iii) physical capital b) Even if the firm owns the robots already and the workers are on salary contracts, explain why there is still an opportunity cost to allocate robots and workers to the production of the K'jipuktuk bus order. c) Assume, A = 5. Find the equation of the isoquant for the production of Q = 135 new e-buses. Rearrange to get K as a function of L.

Answer 1

.. we conside the production fraction Q(K, L) = AL25 k3/5 a i human capital' worky's training , entunship Programmis etc. . ii) Natul Capitali Natual resom ces such as ain, water, trees, o soilete. : il Physical Capital! Ad Machinery, building etc. be As wage rate and rental rate of capital is not equal, fims have the opportunity to vay labor and capital when wage rate is lown or when rental rate of capital is lown as firm's objective is to minimise costi ☺ Assme A=5 and Q = 135 new e-busis .. Hince, : Q=5225k 3/5 135 = 5 22/5K 3/5 Cams Inne 27 = 22/5 3/5

२१ - ks (२१)% ___० (*) Sk ___२५3 -) . : . iso quart. CS Scanned with main on Tu as the equation of

L= 5, : 93.9 | k: 293 : = 52.8 . 243. 243 = When L= 10 ; k=- | Jun L=20, 2 -3 , (26/3 k = 22:243 - 32.8 24 20) =20, k= up = 40,k= = Ros Listo, k = -- | k: 293 - 243 - 13.1 1. L% (80)% 1. Le ID jk: 243 : 22 = 1.3 (10) La L=120, k: 243 1243 | 243 L%”(Jao) :10. 243 4 | kola L=140,k=, 190 | 243- 0140 ) ) 2 k.293 - 2.2.. | tun L: 160 , 243 1/60)% | L% k = 143 。 2分 tum L=180 L% ngo) | 170)% = {16 Scanned with. CamScanner

Table 1 workns/h 1 ans 148) K (robots/h corobores/ho] 83.8 52.8 10 20 32.8 40 60 20.8 15.9 13.1 .80 11.3 100 120 1.40 10 160 1.8.2 7.6 180 Now we can draw the eso quat. Scanned with CamScanner

14 ,k 83 . 8 به .امه أ۱۶۰۰ . 13.1 ج 3Sر دو 11 1 مه ° { 0 s 10 20 10 50 0 0 10 20 140 150 L |cs Scanned with CamScanner

es es Marginal substitution rate of technical Manila etsa umpk 315k215 MPK . . Hne Q (k; 2) = A2 25 K3/5 Hue A=5 Q (KL = SL 315 k 375 Marginal product is labor . Now MPL = 3Q CK32). 512) (98k 3s ƏL 2 L-375 K 375 Marginal product of Capital, MPK = aa (kul)563) 22/5 K 2/5 at - 312/5 K- 275 Now equation of MRST = MRIS?. mpk = 1-3/5 k. 3/5 2/5 k-2/ . MRTS = 2 X equation of for the negative of stanqut line on the iso quart ist the slope € Now of any like - vi ha - dk = - 21 Scanned with CamScanner

2 now homly rate of labor W=&al hom homly opportunity cost of hining a robot. 03 $3 ) non : Now stor I socost equa Tez WLtok =) Te = L+ 3k Now when Te = 60 , . L- infncept of isocost equation [ substitute k = 07 => 60 = 2 +(340) . =) 2 = 60 whn Te = 60 iso cost k- inancept of equation , substitute 2=0] 60='0+ 3k => k = 20 Joining and k infncept. we get iso cosa salir.com Tel . Now whn, Te= 120, . 2 inancept of iso cost equation [substitute cs Scankcoin] 120= 1.+13 x0) = L= 120 Cam's canner

K-in Ancept of iso cost equation Tsubstitute L=0] : - 120 = 0.+ 3k .=> K= 40 than by joining and ik in Ancept, we get the iso cost line Tez wha Te = 180 h Lain tricept of iso cost line substitute kao : 180= Lt (3x0) =). L= 180 - K- in Incept of iso cose line r substitute 1803 bis 073 k =) K=60 - Joining L and K. in Ancept, we gut the iso cost Да TC3 . wha Te=240 L-inducept of iso cost line. [substitute. k=07 240 = Lit (340) => _-. 240 k-infncept of isocost line [substitute L=0] 240 = 07.3k =) K= 80 Joining and k in Ancept, weget isocost line CS Scanned with : CamScanner

wha Te=300 L-inducept of iso cost line [ k=0] 300 = L + (340) => 22360 K-in incept of iso cost line [ 2=0] 300 = 0+ 3k -> K= 100 ung Land k in tu cept we qut the isocost line Joining Landk Te5 Te ($/hr). L-in Ancept I workeus n. Ik-in Ancept (robots/hr] 60 : T60 20 120. 120 . 40 180 180 60 240 240 80 300 300 100 CS Scanned with CamScanner

2Go - 20. 150 + 1 AO IN Q3s 20 5 10| 150 6010 120 150 180 200 210 250 2309 | 20 | . . 이 등 by The noe of hiring labori 쀼 응 r 를 Scanned with CamScanner