Handout 6 Consumer Theory – Applications, Demand Curve, and Engel Curve This handout contains exercises of - Consumer Theory Things you should know - How to find the optimal consumption bundle in the tabulated question? - How to derive a demand curve? - How to find the relationship of goods consumed and income? Exercises Question 1 (Explaining the Example in Class: Consumer Theory – Tabulated Question Format) Suppose good X and good Y are indivisible, that is, must be consumed in exact units. Quantity Philharmonic Concert (P = 10) Theater (P = 12) (Units) Total Marginal MU/P Total Marginal MU/P Utility Utility Utility Utility 0 0 0 1 10 10 1 20 20 1.67 2 17 7 0.7 35 15 1.25 3 22 5 0.5 45 10 0.83 4 26 4 0.4 50 5 0.42 5 28 2 0.2 50 0 0 6 29 1 0.1 7 27 -2 -0.2 If the income is $100, what is the optimal consumption bundle of each good? Question 2 (Consumption Choice with Multiple Goods) Find Jim’s optimal consumption bundle for the following 4 goods when he has $32 to spend. Goods Price Marginal Utility Marginal Utility Marginal Utility Marginal Utility st from 1 Unit from 2nd Unit from 3rd Unit from 4th Unit Burrito $8 160 40 20 8 Tacos $2 10 10 5 4 Salad $4 40 20 10 10 Soda $1 4 3 3 3 Question 3 (Deriving a Demand Curve) Your income is $100. When the price of good X and good Y are $10 and $5, respectively, you purchase 5 units of good X and 10 units of good Y. When the price of good X decreases to $5, you purchase 15 units of good X and 5 units of good Y. 1. Graphically exhibit the two scenarios explained above in the context of consumer theory. 2. From the diagram drawn in part 1, plot the demand curve in the graph beneath. 3. Suppose the demand curve is linear, write down the equation for the demand curve. 4. Can you conclude anything whether good X and good Y are complements or substitutes? 1 Question 4 (Income and Consumption – The Engel Curve) This question outlines what you will see when we derive the Engel curve for goods. Assuming that the price of goods X and Y remain constant at $10 and $5, respectively. - When income is $100, you consume 6 units of good X and 8 units of good Y. - When income is $150, you consume 10 units of good X and 10 units of good Y. - When income is $200, you consume 9 units of good X and 22 units of good Y. 1. Graphically exhibit the three scenarios given above in the context of consumer theory. 2. As income increases from $100 to $150, what can we say about the characteristic of good X? 3. As income increases from $150 to $200, what can we say about the characteristic of good Y? 4. From the diagram drawn in part 1, plot the curve exhibiting the relationship between income and quantity of good X consumed, putting the quantity of good X on horizontal axis. This is known as the Engel curve. 2