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(a) (b) (c) 1/3 1/3 Derek has utility for good 1 and good 2 given by u = x₁x₂. What is Derek's Marginal Rate of Substitution, d2 ? dx₁ When ₁2 and 2 = 8, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? = 8 and ₂ When 1 get 1 extra unit of good 1? = 1, how much of good 2 is Derek willing to give up to

(a) (b) (c) 1/3 1/3 Derek has utility for good 1 and good 2 given by u = x₁x₂. What is Derek's Marginal Rate of Substitution, d2 ? dx₁ When ₁2 and 2 = 8, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? = 8 and ₂ When 1 get 1 extra unit of good 1? = 1, how much of good 2 is Derek willing to give up to

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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10. Derek has utility for good 1 and good 2 given by u = x1/³x/³. (d) (e) What is Derek's Marginal Rate of Substitution, dr2? When ₁ = 2 and x2 = 8, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? (c) When x₁ = 8 and x₂ = 1, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? Explain why the two rates in parts (b) and (c) are different. How are your answers to the above questions different for Derek's friend Joe, who has utility given by v = x²/³x2/³? Solution: a) dx2 X2 I1 dx2 X2 ⇒ dx₂ dx₁ X1 -4dx₁ ⇒ dx₂ -4(1) ⇒ 4 units. c) -(1/4) dx₁ ⇒ dx2 −(1/4)(1) ⇒ 0.25 units. d) When he has a lot of x2 and a little of x₁ in part (b), his marginal utility of x2 is relatively low and his marginal utility of £₁ is relatively high. Therefore, he is willing to give up a lot of x2 to get an additional unit of x₁. The opposite is true in part (c). e) They would not change; Joe's utility is a monotonic transformation of Derek's. dx2 dx1 = X2 I1 →dx₂ - = =
Transcribed Image Text:10. Derek has utility for good 1 and good 2 given by u = x1/³x/³. (d) (e) What is Derek's Marginal Rate of Substitution, dr2? When ₁ = 2 and x2 = 8, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? (c) When x₁ = 8 and x₂ = 1, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? Explain why the two rates in parts (b) and (c) are different. How are your answers to the above questions different for Derek's friend Joe, who has utility given by v = x²/³x2/³? Solution: a) dx2 X2 I1 dx2 X2 ⇒ dx₂ dx₁ X1 -4dx₁ ⇒ dx₂ -4(1) ⇒ 4 units. c) -(1/4) dx₁ ⇒ dx2 −(1/4)(1) ⇒ 0.25 units. d) When he has a lot of x2 and a little of x₁ in part (b), his marginal utility of x2 is relatively low and his marginal utility of £₁ is relatively high. Therefore, he is willing to give up a lot of x2 to get an additional unit of x₁. The opposite is true in part (c). e) They would not change; Joe's utility is a monotonic transformation of Derek's. dx2 dx1 = X2 I1 →dx₂ - = =
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10. (a) (c) 1/3 1/3 Derek has utility for good 1 and good 2 given by u = x₁x₂ dx2? What is Derek's Marginal Rate of Substitution, When 1 = 2 and 2 8, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? = When 1 = 8 and ₂ = get 1 extra unit of good 1? Explain why the two rates in parts (b) and (c) are different. How are your answers to the above questions different for Derek's friend Joe, who has utility given by v = x²/³x2/³? Solution: dx2 dz₁ 1, how much of good 2 is Derek willing to give up to dx2 dx₁ x2 I1 −4(1) ⇒ 4 units. c) da ⇒ dx₂ -4dx₁ ⇒ dx2 -(1/4)dx₁ ⇒ dx₂ -(1/4)(1) ⇒ 0.25 units. d) When he has a lot of x2 and a little of x₁ in part (b), his marginal utility of x2 is relatively low and his marginal utility of x₁ is relatively high. Therefore, he is willing to give up a lot of 2 to get an additional unit of ₁. The opposite is true in part (c). e) They would not change; Joe's utility is a monotonic transformation of Derek's. X2 x2 I1 = ⇒ dx₂ - = = =
Transcribed Image Text:10. (a) (c) 1/3 1/3 Derek has utility for good 1 and good 2 given by u = x₁x₂ dx2? What is Derek's Marginal Rate of Substitution, When 1 = 2 and 2 8, how much of good 2 is Derek willing to give up to get 1 extra unit of good 1? = When 1 = 8 and ₂ = get 1 extra unit of good 1? Explain why the two rates in parts (b) and (c) are different. How are your answers to the above questions different for Derek's friend Joe, who has utility given by v = x²/³x2/³? Solution: dx2 dz₁ 1, how much of good 2 is Derek willing to give up to dx2 dx₁ x2 I1 −4(1) ⇒ 4 units. c) da ⇒ dx₂ -4dx₁ ⇒ dx2 -(1/4)dx₁ ⇒ dx₂ -(1/4)(1) ⇒ 0.25 units. d) When he has a lot of x2 and a little of x₁ in part (b), his marginal utility of x2 is relatively low and his marginal utility of x₁ is relatively high. Therefore, he is willing to give up a lot of 2 to get an additional unit of ₁. The opposite is true in part (c). e) They would not change; Joe's utility is a monotonic transformation of Derek's. X2 x2 I1 = ⇒ dx₂ - = = =
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