Question

II. A simple economy with two factor inputs and two outputs. Let there be two factor inputs: land denoted T and labor denoted L. The resource endowment of T is Tº = 8; the resource endowment of L is Lº = 8. Let there be two goods: z and y. Robinson has a utility function u(x,y) := xy. The prevailing wage rate of labor is w, and the rental rate on land is r. Good is produced in a single firm by the production function x=f(L",1") :=1 + (L"T")1/2, where L' is L used to produce x, Tis T used to produce r. f(L",") > O for L" > 0, Tr> 0; f(0,0) = 0. Good y is produced in a single firm by the production function y = 9(LY, T') := 1 + (LMT)1/2, where LV is L used to produce y, TY is T used to produce y. g(LV,TV) > 0 for LV > 0,T" > 0; 9(0,0) = 0. The price of good is p. The price of good y is p. Profits of firm x are II" =p f(L",T)-wL"-TT". Profits of firm y are IIV = p'g(LV,TV)-WL-TV. Robinson's income then is wL+rT +11° + ITV. Assume f. 9, u, to be strictly concave, differentiable. Assume all solutions are interior solutions. Subscripts denote partial derivatives. An efficient allocation in the economy is characterized by maximizing the Lagrangian, V with Lagrange multipliers a, b, c, d, P = u(x, y) +a[c – f(L*,T")] + [ = g(L",T)] + c(L° – LÝ – LP) +d(T2 – T –T").

Answer 1

ANSWER The Competitive critession in the market place is a case scensario where in the maxlect structure many business sell a homogenous product Competitively without battico entry to the market. The purpose of resource allocation is to promote efficient and management of seasie resources available, it also entails proper utilization of the resources The rules of the game" associated with masket Isansaction's osci- * An example where the markect exchange is unable to allocate de soutic effictively in a slenatio , where the government takes control of the market by imposing high taxes on certain commodities for instance sugar. The Competitive critersion for this scenatio is the Competition between the government and private investors.