Exam1_Solution - = w Y Y Nw = w b(b L = 2 Y N N w b-Y-Nw...

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Intermediate Micro Analysis: Exam 1 - Solution Bin Xie Mar. 5 2015 Version A: 1.C 2.A or C 3.C 4.A 5.C 6.D 7.D 8.C 9.D 10.C or D Version B: 1.B 2.D 3.D 4.D 5.A 6.B 7.A or B 1
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8.D 9.D 10.A or B 1. Solution: (a) First, compute the before-tax equilibrium price by equating the de- mand to the supply: 150 + 10 p = 900 - 20 p , p * = 25 and Q * = 400 . Consumer surplus: CS = ( ¯ P - P * ) Q * / 2 = (45 - 25) * 400 / 2 = 4000 . (b) After-tax equilibrium: 150 + 10( p - τ ) = 900 - 20 p . p 0 = 25 + 1 / 3 τ and Q 0 = 400 - 20 / 3 τ . (c) Tax incidence on consumers: p 0 - p * = 1 / 3 τ . Tax incidence on suppliers: 2 / 3 τ . (d) TR = τQ * = τ (400 - 20 / 3 τ ) (e) Maximization: dTR = 400 - 40 / 3 τ = 0 . τ * = 30 . Second order condition satisfied. 2. Solution: (a) L = 10 q 1 / 2 1 + q 2 + λ ( Y - p 1 q 1 - p 2 q 2 ) . Solve the F.O.Cs: MRS = - 5 q - 1 / 2 1 = - p 1 p 2 = MRT . The demand function of good 1 is q 1 = 25 p 2 2 p 2 1 . The demand function of good 2 is q 2 = Y - p 1 q 1 p 2 = Y p 2 - 25 p 2 p 1 = 200 p 2 - 25 p 2 p 1 . (b) q * 1 = 100 and q * 2 = 50 . U * = 150 . (c) New price levels: p 0 1 = 2 and p 0 2 = 2 . q 0 1 = 25 and q 0 2 = 75 . U 0 = 125 . (d) H 1 = ∂E ∂p 1 = 25 p 2 2 p 2 1 . Δ H = H 0 1 - H * 1 = 25 - 100 = - 75 . (e) EV = E ( p 1 , p 2 , U 0 ) - Y = (250 - 100) - 200 = - 50 . 2
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3. Solution: (a) H + N = 1
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Unformatted text preview: = w + Y * Y + Nw = w + b (b) L = 2 Y N + N + λ ( w + b-Y-Nw ) . Solve the F.O.Cs: MRS =-2 Y + 1 2 N =-w = MRT . N = 1 + 2 b 4 w + 1 2 . H = 1-N = 1 2-1 + 2 b 4 w . Y = w + b 2-1 4 . (c) ∂H ∂b =-1 2 w . The labor supply will decrease when unearned income increases. (d) ∂Y ∂b = 1 2 . The consumption will increase when unearned income increases. (e) ∂H ∂w =-1 + 2 b 4 w 2 =-11 4 w 2 . Positive effect of increase in wage on labor supply and meanwhile negative effect on leisure. It indicates that (1)either substitution effect (-) and income effect (-) are in the same direction and L is a inferior good; (2) or substitution effect (-) dominates income effect (+) and L is a normal good. 3...
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