1. Assume that a typical very nicely behaved consumer…

a)See bundle A.

b)The new budget line is BLsub and since we said in class to assume that Housing is normal, then you know that the new bundle must be on BLsub to the right of A’, so suppose it is B. Note the government must then spend a total of distance BC in $aog for the program.

c)Now the government gives you distance DE in dollars and you end up at bundle D.

d)Since DE=FCBC, the government spends more with the housing subsidy program in part (b).

e)If the government’s goal is to stimulate the hosing market, use the plan in (b) since B has to be to the right of D on the indifference curve ICafter.

  1. Assume that Abe has the following utility function: u=y+x1/2

a)Abe is nicely behaved but not very nicely behaved since his indifference curves will crash into the axes.

b)Note: MUy=1 and MUx=.5x-.5and that MRS=MUx/MUy=.5x-.5. Note that ERS=Px/Py. Now set MRS=ERS and solve and you get: .5X-.5 = Px/Py X*=Py2/4Px2 and then using the budget constraint you get: Y*=I/Py – (Py/4Px).

c)Notice: 1) for an “interior” solution, you must check that Abe has enough income, given Px and Py to afford the bundle X*. 2) X* does not depend on income (at an interior solution) or you can say there would be no income effect for X* (at an interior solution).

  1. Suppose not. Suppose both goods X and Y are inferior. Now suppose that income increases. You would buy less of both X and Y. This would imply that you would be beneath your budget constraint, which in inconsistent with the notion of monotonicity. So it can not be the case that both goods are simultaneously inferior, if there are only 2 goods in the consumption bundle.
  2. Let the Px=1 and Py=1 and note that the ERS=1 and note that we can infer that I=180. Now notice that Px=1.40 and Py=.50 and now the ERS=2.8. Also notice that at Px=1.40 and Py=.50, the consumer can STILL afford the same original bundle X=100 and Y=80. So the new budget line goes through the original bundle but with a steeper slope than the original budget line, generating bundles that are now affordable and in the “better than set” relative to the original indifference curve. Note all these better bundles will involve X<100. So the consumer MUST buy fewer units of X. (Make sure you can draw this one – looks just like a Slutsky-style substitution effect.)