4. 40 points total. Suppose there are two types of families in a commu- nity. Type A families have income 300, type B families have income 900. Both families share the same utility function over education and other goods: U(G, E) = = InG + 2 In E, Both goods have price $1. (a) Write out the consumer problem faced be each family. 10 points. (b) Construct the Lagrangian and find the amount of education each household would choose in a private market for education. Verify your solution is correct. 5 points. (c) Depict the solution you found graphically. 5 points. 7 150 (d) Suppose this community decides to make available 150 units of education, for free. Which households will send their child to public school? Is there any crowding out? If so, how much? 5 points. (e) Suppose instead they community makes available a $150 dollar voucher, than can be used either at the public school (if E = 150 is chosen), or at a private school. Depict this new situation graphically. 5 points. (f) How much education will each family choose under this policy? 5 points. Which policy (public school or vouchers) would you recommend? What are some arguments for or against each policy? 5 points