Handout 5 Consumer Theory – Budget Lines, Indifference Curves, and Optimal Consumption Rule This handout contains exercises of - Budget Line (Budget Constraint, Budget Set) - Consumer Theory Things you should know - How to draw a budget line? What shifts and rotates a budget line and how? - What are total and marginal utility? What is the law of diminishing marginal utility? - What is indifference curve? What is the meaning of its slope? - How to find the optimal consumption bundle (consumer equilibrium) in both tabulated and equation question formats? Exercises Question 1 (Budget Line Basics) 1. Write down the equation for the budget line of two goods, when one has an income of $200, the price of good X is $5 and the price of good Y is $10. What is the slope of this budget line? 2. What happens to the budget line if the price of good X decreases from $5 to $2.5? 3. What happens to the budget line if the price of good Y increases from $10 to $20? 4. What happens to the budget line if the income decreases to $100? 5. What happens to the budget line if one has an income of $100, the price of good X is $2.5 and the price of good Y is $5? Question 2 (Consumer Theory – Tabulated Question Format) Suppose good X and good Y are indivisible, that is, must be consumed in exact units. Quantity Good X Good Y (Units) Total Marginal Total Marginal Utility Utility Utility Utility 0 0 0 1 50 40 2 80 60 3 100 70 4 110 75 1. Fill in the marginal utilities in the table above. Suppose the price of good X is $5, the price of good Y is $10 2. If the income is $40, what is the optimal consumption bundle of good X and Y? 3. If the income is $25, what is the optimal consumption bundle of good X and Y? 4. If the income is $30, what is the optimal consumption bundle of good X and Y? Question 3 (Consumer Theory – Conceptual Question) If price of good X is $10, and price of good Y is $20 1. What is the marginal rate of substitution of the optimal consumption bundle? 2. If currently the marginal rate of substitution (MUX/MUY) is 4, then one is consuming [ too much / too few ] of good X and [ too much / too few ] of good Y. 3. If currently the marginal rate of substitution (MUX/MUY) is 0.5, then one is consuming [ too much / too few ] of good X and [ too much / too few ] of good Y. 1 Question 4 (Consumer Theory – Equation Question Format) 1. There are two goods to be consumed, X and Y, at price PX and PY, respectively. Write down the condition which yields the maximum happiness. Explain the happiness formula. 2. The marginal rate of substitution is given by MRS = MUX/MUY = 3Y/X. If prices of good X and good Y are $10 and $5, respectively, and you have the income of $120, what is your optimal consumption bundle? Also draw the solution in the budget line and indifference curve. 3. If prices of good X and good Y are $20 and $10, respectively, and you have the income of $240, what is your optimal consumption bundle? (Hint: If it takes you more than 5 seconds for this part, you must have been zoning out in class!) 2