# s06-answers-midterm1-4 - Economics 302 Intermediate...

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Economics 302 Silve Parviainen Intermediate Microeconomics Spring 2006 Answers to Midterm Examination I 1 Demand and Elasticity (a) 100 10 p g 10(2) + 5(2) = 40 p g 20 = p g = 110 5 =2 . 2 Q = 100 10(2 . 2) 10(2) + 5(2) = 68 . (b) ± q,p = ∂Q d g ∂p g p g Q d g = 10 2 . 2 68 ≈− 0 . 32 . Since | ± | < 1, demand is inelastic. Green beans are a necessary good for this consumer. In a case of a price increase, the percentage drop in consumption will be smaller than the price increase. (c) ± q g ,p c = d g c p c Q d g = 10 2 68 = 20 68 < 0 ± q g ,p b = d g b p b Q d g =5 2 68 = 10 68 > 0 , beans and carrots are demand complements and beans and broccoli demand substitutes. 2 Consumer Optimum (a) u ( m, p )=min { m, p 2 } . (b) In the optimum m = p 2 . Plugging that in the budget line for m yields p m p 2 + p p p = I = p = I p m 2 + p p and m = p 2 = I p m +2 p p . With p m =8 ,p p =5and I = 180, m = 180 8+10 =10 and p = 180 8 2 +5 = 20. (c) When p m m = 180 5+10 =12 and p = 180 5 2 +5 =24 . (d) All is due to income eFect. ±or perfect complements the substitution eFect is zero. (e) See Graph (1).

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3 Income and Substitution Efects (a) For u ( x 1 ,x 2 )= x 1 x 2 the optimality condition MRS = p 1 p 2 is x 2 x 1 = p 1 p 2 = x 2 = p 1 p 1 x 1 . Substituting this into the budget line for x 2 yields p 1 x 1 + p 2 ± p 1 p 2 x 1 ² = I = x 1 = I 2 p 1 and x 2 = I 2 p 2 . With the given prices and income
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