Suppose that a consumer has utility given by U(X, Y ) = XY + 10Y and...

Suppose that a consumer has utility given by U(X, Y ) = XY + 10Y and income of $100 to spend on goods X and Y.
1. The prices of X and Y are both $1 per unit. Use a Lagrangian to solve for the optimal basket of goods.
2. 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.
3. 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?
4. Find the income effect of the increase in the price of good X on the consumption of each goo Are the goods normal or inferior?

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Rahul Sunny answered 2 years ago

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