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# answers-midterm1 - Economics 302 Silve Parviainen...

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Unformatted text preview: Economics 302 Silve Parviainen Intermediate Microeconomics Spring 2007 Answers to Midterm Examination I 1 Preferences and Utility (a) u ( a, o ) = 2 a + o . See Graph (1) (b) u ( a, o ) = a . See Graph (2) (c) u ( a, o ) = min { a, 3 2 o } . See Graph (3) (d) u ( a, o ) = ao . See Graph (4) 2 Utility Maximization (a) The optimality condition MRS = MU 1 MU 2 = p 1 p 2 yields x 2 = p 1 p 2 x 1 . Substituting this for x 2 in the budget line gives p 1 x 1 + p 2 p 1 p 2 = I = ⇒ x 1 = I 2 p 1 and x 2 = p 1 p 2 I 2 p 1 = I 2 p 2 . (b) For p 1 = p 2 = 4 and I = 32, x 1 = 32 2(4) = 4 and x 2 = 32 2(4) = 4 . (c) x 1 = 32 2(8) = 2 and x 2 = 4 . (d) First, determine the level of utility reached at (c): u (4 , 4) = 4 1 2 4 1 2 = 4. Now p − 2 can be determined from 4 = s 32 2(8) 32 2( p 2 ) = r 2 16 p 2 = ⇒ p 2 = 2 . 3 Consumer Optimum II (a) u ( g, v, r ) = min { 1 6 g, 1 2 v, r } . (b) At the optimum, 1 6 g = r = ⇒ g = 6 r 1 3 v = r = ⇒ v = 3 r 1 6 g = 1 3 v....
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answers-midterm1 - Economics 302 Silve Parviainen...

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