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