= Biln(x - n) + A consumer's preferences for two goods are represented by the function...

 

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= Biln(x₁ - n) + A consumer's preferences for two goods are represented by the function In u=, B2ln(x2-12) where B₁, B2>0 and ₁ + 2 = 1 and x₁>20, x2 > 2≥0. The Linear Expenditure System (LES) may be derived from this function. LES was first used by Richard Stone (1954): Linear Expenditure System and Demand Analysis: An Application to the Pattern of British Demand, The Economic Journal, 511-527. Furthermore, the Cobb- Douglas (CD) utility function may be written as In u= alnxi + a₂lnx₂. a) The CD-utility function is a special case of the LES-utility function. Show this. b) Derive the ordinary demand functions from the CD-utility function. c) Derive the ordinary demand functions from the LES-utility function. d) Compare the LES and CD demand functions. e) Assume a Cobb-Douglas utility function. Derive the own-price, cross-price and income elasticities in the two good case. f) Assume a LES utility function. Derive the own-price, cross-price and income elasticities in the two good case (the own-price elasticities are tricky). g) Show that the elasticities derived from the LES utility function indicate that we have no inferior goods, only gross complements, and own-price inelastic demand. = Biln(x₁ - n) + A consumer's preferences for two goods are represented by the function In u=, B2ln(x2-12) where B₁, B2>0 and ₁ + 2 = 1 and x₁>20, x2 > 2≥0. The Linear Expenditure System (LES) may be derived from this function. LES was first used by Richard Stone (1954): Linear Expenditure System and Demand Analysis: An Application to the Pattern of British Demand, The Economic Journal, 511-527. Furthermore, the Cobb- Douglas (CD) utility function may be written as In u= alnxi + a₂lnx₂. a) The CD-utility function is a special case of the LES-utility function. Show this. b) Derive the ordinary demand functions from the CD-utility function. c) Derive the ordinary demand functions from the LES-utility function. d) Compare the LES and CD demand functions. e) Assume a Cobb-Douglas utility function. Derive the own-price, cross-price and income elasticities in the two good case. f) Assume a LES utility function. Derive the own-price, cross-price and income elasticities in the two good case (the own-price elasticities are tricky). g) Show that the elasticities derived from the LES utility function indicate that we have no inferior goods, only gross complements, and own-price inelastic demand.

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The detailed answer for the above question is provided below A The CobbDouglas CD utility function can be written as In u alnx lnx2 This is a special case of the Linear Expenditure System LES utility ... View the full answer