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1. At the optimum point for a representative consumer, why must the marginal utility per TL spent on all goods be the same? (Support your explanation with graphs and formula/equations where necessary.)
2. Consumer A has preferences for food F and clothing C described by a utility function:
U (F, C) =FC. Suppose that food costs 1 TL a unit and that clothing costs 2 TL a unit. She has 12 TL to spend on food and clothing.
a) Using algebra (the tangency condition and the budget line), find the optimal choice of food and clothing.
b) What is the marginal rate of substitution of food for clothing at her optimal basket? Show this graphically and algebraically.
c) Suppose she decides to buy 4 units of food and 4 units of clothing with her 12 TL budget (instead of the optimal basket). Would her marginal utility per dollar spent on food be greater than or less than her marginal utility per dollar spent on clothing? What does this tell you about how she should substitute food for clothing if she wanted to increase her utility without spending any more money?
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