Question

A firm has a Cobb-Douglas production function q = AKL, where K denotes capital, L is labor, and A, a, b, are constants. ginal returns to labor in the short run if its production function is 1. Sketch an isoquant line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 2. On a separate graph, draw an isocost line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 3. On a third graph, draw both isoquant and isocost showing (i) the optimal condition and (ii) provide its interpretation; also indicate the quantity of the inputs (K, and L). 4. Given that the unit cost of labor is w and for capital is r, using the Lagrangian method solve for the cost minimizing inputs (K, and L).

Answer 1

1. 
   a q = f(1) Classicals S 9= f(lik) → Neo Classicals - To produce any output we have to incure cost fore hiring the factors of production. - Suppose wages of labour is w and interest of capital is de and our total cost is a WLtek Lc WLt&k=c Isocost squation cal k= WL > bocast line equation Suppose e=100 , W=5, e=10 =) K= 100 - EL slope of iso cost = - 1 which shows the change 10/10,10) ink by an unit change in h which the factor Isocost market allows » Isocost shows the minimum cost and maximum brodo roduction. 5 (200) 15 20 10
   
   HOBBimal Combination slobe of isooyont is equal to the slote of socant line 12 koguant a point 'a is the affinal choice at CQ MRTS = and x* and t are the optimal combinations of L&K
   
   q= Akab ky capital مطما دا Asad are constrants Isoquant of the cobb- Douglas production function q= Akab is given by the below diagram Slope of an isoquant is gonen by its MRTs which is equal to the ratio a marginal products of Labour and capital. MRTS = MP LK MPKI DL MPL =Dq= Ab ka (k-1 = b Aka 2 h = bal MPx = 0 = Aakal b = a Akh_ amark MRTS = bvh = 4.8x = boleh MRTS LK = bke Slope represents the change mkoby a whid Change in t which the technique of production allows S Scanned with CamScanner
   
   a q = f(1) Classicals S 9= f(lik) → Neo Classicals - To produce any output we have to incure cost fore hiring the factors of production. - Suppose wages of labour is w and interest of capital is de and our total cost is a WLtek Lc WLt&k=c Isocost squation cal k= WL > bocast line equation Suppose e=100 , W=5, e=10 =) K= 100 - EL slope of iso cost = - 1 which shows the change 10/10,10) ink by an unit change in h which the factor Isocost market allows » Isocost shows the minimum cost and maximum brodo roduction. 5 (200) 15 20 10
   
   HOBBimal Combination slobe of isooyont is equal to the slote of socant line 12 koguant a point 'a is the affinal choice at CQ MRTS = and x* and t are the optimal combinations of L&K
   
   q= Akab ky capital مطما دا Asad are constrants Isoquant of the cobb- Douglas production function q= Akab is given by the below diagram Slope of an isoquant is gonen by its MRTs which is equal to the ratio a marginal products of Labour and capital. MRTS = MP LK MPKI DL MPL =Dq= Ab ka (k-1 = b Aka 2 h = bal MPx = 0 = Aakal b = a Akh_ amark MRTS = bvh = 4.8x = boleh MRTS LK = bke Slope represents the change mkoby a whid Change in t which the technique of production allows S Scanned with CamScanner