Someone Answer Me!!!!!

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HEY THERE! i intend to write the DSE entrance test, but when i went thru their old question papers i had no clue abt half the stuff in it ( illustrated as follows) . the r8 answers r given, but no idea hw one gets there.wud REALLY REALLY appreciat...
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Dude do u think u can start a thread fro answering single question... there is something called "search" in this forum which u can use to find relevant threads to post ur queries
Mods please look into this :neutral:

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HEY THERE! i intend to write the DSE entrance test, but when i went thru their old question papers i had no clue abt half the stuff in it ( illustrated as follows) . the r8 answers r given, but no idea hw one gets there.wud REALLY REALLY appreciate it if someone cud tell me. its URGENT!!!!

Consider a competitive exchange economy with 2 agents( 1 & 2) & 2 goods (X & Y) . Agent 1s endowment is(100,100) & agent 2s endowment is( 50,0). An allocation for agent i. is denoted (xi, yi) ,where xi is his allocation of X & yi is his allocation of Y. Agent 1s objective is to choose (x1,y1) to maximize his utility min{x1,y1}. Agent 2s objective is to choose (x2,y2) to maximize his utility x2+y2.
Answer the following questions on the basis of the above information:
1) an example of competitive equilibrium allocation for this economy is
a) (x1,y1) = (100,50) & (x2,y2) = (50,50)
b) (x1,y1) = (125,100) & (x2,y2) = (25,0)
c) (x1,y1) = (50,50) & (x2,y2) = (100,50)
d) (x1,y1) = (100,100) & (x2,y2) = (50,0)
ans: d.
2) an example of pareto efficient allocation for this economy is
a) (x1,y1)= (50,50) & (x2,y2) = (100,50)
b) (x1,y1) = (125,100) & (x2,y2) = (25,0)
c) (x1,y1) = (125,75) & (x2,y2) = (25,25)
d) (x1,y1) = (50,100) & (x2,y2) = (100,0)
ans: (a)
3) an example of a pair of competitive equilibrium prices( p1, p2) for this economy is
a) (1,0)
b) (0,1)
c) ( 1/3,2/3)
d) (2/3,1/3)
ans: ( 0,1)
4) suppose the govt. imposes a lumpsum tax of rs 50 on agent 1 and transfers the tax receipts as a lump sum subsidy of rs 50 to agent 2. After this wealth transfer, an example of a competitive equilibrium for this economy is: prices = (1/2,1/2) & allocation:
a) (x1,y1) = (100,100) & (x2,y2) = (50,0)
b) (x1,y1) = (50,50) & (x2,y2) = (100,50)
c) (x1,y1) = (0,100) & (x2,y2) = (150,0)
d) (x1,y1) = (100,0) & (x2,y2) = (50,100)
ans: (a)

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