You can't really draw indifference curves for Lexicographic preferences as they are just single points. There will be 1 competitive equilibrium in the 6th question. If the prices ratio px/py>0, then in any case, agent 1 will always spend all his money on buying good x whereas agent 2's consumption bundles would consume equal units of good x and good y.
x1(consumer 1's demand of good 1)= 10py/px y1(consumer 1's demand of good 2)=0
x2(consumer 2's demand of good 1)= 11px/px+py=consumer 2's demand of good 2)= 11py/px+py
now, x1+x2=11 and y1+y2=10
You may solve this to get the competitive equilibrium.
When px=1, py=0, Agent 2 would want 11 units of good 2 to maximise utility (since they are free), there will no equilibrium. When px=0 py=1, agent 1 would demand infinite amounts of good 2 as more units give him more utility and they are free. So again, we're left with that one case.
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