1 Suppose that a consumer has utility given by U ( X , Y ) XY 10 Y and income of $100 to spend on goods X and Y a The prices of X and Y are both $1 per unit Use a Lagrangian to solve for the optimal basket of goods b Suppose that the price of X increases to $5 per unit Use a Lagrangian to solve for the new optimal basket of goods Find the total effect of the price change on the consumption of each good c Use a Lagrangian to find the substitution effect of the increase in the price of good X on the consumption of each good What income would the consumer need to attain the original level of utility when the price of X increases to $5 per unit d Find the income effect of the increase in the price of good X on the consumption of each good Are the goods normal or inferior Explain e Show that the total effect of the increase in the price of X is equal to the sum of the substitution effect and the income effect f Develop the graphical solution for parts d and e, labeling the substitution, income and total effects Interpret

Question

1 Suppose that a consumer has utility given by U ( X , Y )   XY   10 Y and income of $100 to spend on goods X and Y   a The prices of X and Y are both $1 per unit  Use a Lagrangian to solve for the optimal basket of goods  b Suppose that the price of X increases to $5 per unit  Use a Lagrangian to solve for the new optimal basket of goods  Find the total effect of the price change on the consumption of each good  c Use a Lagrangian to find the substitution effect of the increase in the price of good X on the consumption of each good  What income would the consumer need to attain the original level of utility when the price of X increases to $5 per unit  d Find the income effect of the increase in the price of good X on the consumption of each good  Are the goods normal or inferior  Explain  e Show that the total effect of the increase in the price of X is equal to the sum of the substitution effect and the income effect  f Develop the graphical solution for parts d and e, labeling the substitution, income and total effects  Interpret

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1.Suppose that a consumer has utility given by U ( X , Y ) = XY + 10 Y and income of $100 to spend

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