Hugo's utility function for food and shelter is defined by F 2 S 3 . The price of food is $1 per unit and the price of shelter is $10 per unit. Hugo's Income is $100. Food and Shelter may be purchased in fractions.
- Set up the maximization problem and the accompanying Lagrangian.
- Are Hugo's preferences convex? Justify your answer.
- How much food and shelter will Hugo consume?
- Suppose the price of food increases to $1.50. How much food and shelter will Hugo now consume?
- What is the income effect versus the substitution effect on F from the price change? Depict the two effects on a graph.