# h3_ans - S has not changed S does not change 3(a PB = 2J...

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1 The Colorado College Department of Economics and Business Block 7 Econ 207 HW 3 ans. 1. (a) The consumer’s Lagrangian function is given by ] 4 2 100 [ 2 1 6 . 2 4 . 1 q q q q L - - + = λ 6 . 1 2 6 . 2 6 . 1 1 ) ( 2 . 0 2 4 . 0 q q q q dq dL = = - = - (1) 4 . 2 1 4 . 2 4 . 1 2 ) ( 15 . 0 4 6 . 0 q q q q dq dL = = - = - (2) 0 4 2 100 2 1 = - - = q q d dL (3) Equating (1) and (2), 4 . 2 1 6 . 1 2 ) ( 15 . ) ( 2 . q q q q = 15 . ) ( 2 . 15 . ) ( ) ( 2 . 1 2 4 . 1 2 6 . 1 2 = = q q q q q q 1 2 75 . 0 q q = Using the above relationship in (3) 100 = 2q 1 +4(.75q 1 ) 100 = 2q 1 +3q 1 q 1 = 20 q 2 = .75(20) = 15 . (b) U = (20). 4 (15) .6 = 3.31(5.08) = 16.814 2. (a) Since the Jones family spends two-thirds of their income on shelter and one-third on food we have: 3 3 2 2 3 3 F F S S I I P F or F P I I P S or S P = = = = Both functions are homogeneous of degree zero in income and prices. For example: 2 (2 ,2 ,2 ) ( , , ) 3(2 ) 3 F s F S F F I I F P P I F P P I P P = = = (b) If I = 20000 F = 6,667/P F S = 13,333/P S (c) If I = 50,000

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2 F = 16,667/P F S = 32,333/P S (d) The demand functions derived in (a) that P F does not enter into the shelter demand function. Since food always constitutes 1/3 of income, a change in P F with no change in I does not change spending on either food or shelter. Since P
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Unformatted text preview: S has not changed, S does not change 3. (a) PB = 2J and .05PB + .1J = 3 5PB + 10J = 300 PB + 2J = 60 4J = 60 J = 15, PB = 30 (b) P J = \$.15 PB = 2 J .05 PB + .15 J = 3 5 PB + 15 J = 300 25 J = 300 J = 12, PB = 24 (c) To continue buying J = 15, PB = 30, David would need to buy 3 more ounces of jelly and 6 more ounces of peanut butter. Should increase his allowance by: 3(.15) + 6(.05) = \$.75. (d) 4. (a). U 2005 = 40 40 × = 40 U 2006 = 20 80 × = 40 J PB 12 30 24 15 3 (b) 2005 2006 ('05 ) 1(40) 1(40) 80 ('05 ) 1(20) 1(80) 100 I prices I prices = + = = + = “real income” has risen. (c). 2005 2006 ('06 ) 4(40) 1(40) 200 ('06 ) 4(20) 1(80) 160 I prices I prices = + = = + = “real income” has fallen....
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## This homework help was uploaded on 04/19/2008 for the course EC 207 taught by Professor Ghosh during the Spring '08 term at Colorado College.

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h3_ans - S has not changed S does not change 3(a PB = 2J...

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