Ex/UG/Eco/32/2013 BACHELOR OF ARTS EXAMINATION, 2013 (2nd Year, 3rd Semester) ECONOMICS (Honours) Course - UG / Eco - 32 ( General Equilibrium and Welfare Economics ) Time : Two Hours Full Marks : 30 The figures in the margin indicate full marks. Section - A Answer any three questions. 1. In a two person two good pure exchange economy give an example (using figure) : (i) where General / Walrasian equilibrium does not exist and (ii) where the General / Walrasian equilibrium is unstable. 2½+2½ 2. Can a collective action which harms a majority satisfy the Kaldor-Hicks criterion? Why? Will such an action be approved by majority vote? Could it be approved if the buying of votes by gainers and selling of votes by losers were permitted? 1+1+1+2 [Turn over] 6 /2 - 125 [ 2 ] 3. Four firms located at different points on a river dump various quantities of effluent into it. The effluent adversely affects the fishing for fishermen who live downstream. As a policy advisor for a regional planning organization, how would you compare and contrast the following options for dealing with the harmful effect of the effluent : (a) An equal rate effluent fee on firms located on the river (b) An equal standard per firm on the level of effluent that each can dump (c) A transferable effluent permit system in which the aggregate level of effluent is fixed and all firm receives identical permits. 5 4. Show that in case of three alternatives neither majority voting rule nor rank order voting rule as a method of social choice can satisfy five axioms laid down by Arrow. 5 Section - B Answer any three of the following. 5. Assume the aggregate demand and supply functions are given by D  25 / p and S  5 p . Is the dynamic process locally stable? 5 [Turn over] 6/2 - 125 [ 3 ] 6. Consider a two person, two commodity pure exchange economy with U1  q11 q12 q21 q22  , U 2  q21q22 , q11  q21  q10 and q12  q22  q2 0 . Derive the contract curve of Pareto optimal allocations as an implicit function of q1 and q2. If first person is endowed with q10 of first good and 0 unit of second good and second person is endowed with 0 unit of first good and q20 unit of second good, find out the general equilibrium solution. Does the general equilibrium satisfy Pareto optimality condition ? 2½+2½ 7. Consider a two person (A and B) two good (good 1 and good 2) exchange economy. Suppose the utility functions of two individuals are given by U A  x1A x 2A and U B  x1B x B2 . b g b g The initial endowments are  A  1, 0 and  B  0, 1 . Find out the equation of utility possibility frontier (UPF). In order to maximize a ‘‘Nietzschean social welfare function’’ b g l W U A , U B  max U A ,U B q what would be the chosen UA and UB ? In order to maximize a ‘‘Rawlsian social welfare function’’ b g l W U A , U B  min U A ,U B q what would be the chosen UA and UB ? Are these two social welfare function Pareto rankable ? 2+1+1+1 8. Falta, a highly productive fishing area can be divided into two zones in terms of fish population. The daily fish catch in Zone 1 is F1 = 200X1 – 2(X1)2 [Turn over] 6 /2 - 125 [ 4 ] and daily fish catch in Zone 2 is F2 = 100(X 2) – (X2)2 where Xi is the number of boats fishing in Zone i = 1, 2. The fish are sold at Rs. 100 per ton. Total cost per boat is constant at Rs. 1000 per day. (i) If the boat is allowed to fish where they want, with no government restriction, how many boats will fish in each zone? What will be the gross value of the catch? (ii) If the West Bengal government can restrict the boats, how many should be allocated to each zone? What will be the gross value of the catch? (iii) Now if 100 boats are licensed by the West Bengal government to fish in these two zones and boats are allowed to fish anywhere, how many boats will fish in each zone? Does it maximize the total value of the catch? 2+2+1 ___________ [Turn over] 6 /2 - 125