Income and Price Effects: Engel Curves and Budget Constraints, Study notes of Microeconomics

Download Income and Price Effects: Engel Curves and Budget Constraints and more Study notes Microeconomics in PDF only on Docsity! -1- LECTURES 22-23: INCOME AND PRICE EFFECTS QUESTIONS AND PROBLEMS True/False Questions ____ The Engel curves of a consumer with Cobb-Douglas utility are linear, while those of a consumer with linear utility are not. ____ A Giffen good is necessarily an inferior good, while the reverse is not necessarily true. ____ The Engel curves of a consumer with Leontief utility are linear, while those of a consumer with Cobb-Douglas utility may or may not be linear. ____ An inferior good is necessarily Giffen, while the reverse is not necessarily true. ____ A good can be a luxury for one consumer, but a necessity for another. ____ A luxury good is necessarily a normal good, while the reverse is not necessarily true. ____ At very low income levels no good is likely to be inferior. ____ Engel curves relate the consumption of X with the price of good Y. ____ The Engel curve relates the demand of a good with the good’s price holding all other prices constant. ____ The income and substitution effects are always working in opposite directions. ____ The income and substitution effects of a price change cancel each other out, at least partially. ____ All luxury goods are normal. ____ All Giffen goods are inferior. ____ The Engel curve for good X is the function that relates a person’s income with that person’s consumption of good X. -2- Short Questions 1. Consider the figure with the following two budget constraints, BC1 and BC2. Consider next the following possibilities: A. Price of X increases and income of the consumer also increases. B. Price of Y decreases and income of the consumer also decreases. C. Price of Y increases and income of the consumer decreases. D. Price of X decreases and income of the consumer remains unchanged. E. Price of X decreases and income of the consumer increases. F. Price of X decreases and income of the consumer also decreases. Which of the above possibilities can lead to a movement of the budget constraint from BC2 to BC1? (Write below the letters that correspond to each scenario that can have the effect stated above.) -5- 4. Consider the figure below, which has two indifference curves, U1 and U2 (U2 corresponds to a high level of utility) and two budget constraints, BC1 and BC2. The dashed line is parallel to BC2 and tangent to U1, while the dotted line is parallel to BC1 and tangent to U2. Answer the following questions with regards to this figure. a. The shift from budget constraint BC2 to BC1 represents an increase in the price of product Y, decrease in income, a decrease in the price of X, or none of the above? b. In the range of prices and real income changes shown in the figure above, is good Y normal or inferior? Explain why (in one sentence or two at most). c. Good X is Giffen. Is this statement true, false, or we can’t tell on the basis of the above figure. Explain in a single sentence. -6- 5. Consider the figure below, which has two indifference curves, U1 and U2 (U2 corresponds to a high level of utility) and two budget constraints, BC1 and BC2. The dashed line is parallel to BC2 and tangent to U1, while the dotted line is parallel to BC1 and tangent to U2. Answer the following questions with regards to this figure. a. The change in the consumption of X due to the substitution effect of the budget constraint shift from BC1 to BC2 is given by (i) X2-X1, (ii) X3-X1, (iii) X3-X2, (iv) X4-X2, or (v) X4- X3? b. In the range of prices and real income changes shown in the figure above, is good X normal or inferior? Explain why (in one sentence or two at most). c. Good Y is Giffen. Is this statement true, false, or we can’t tell on the basis of the above figure. Explain in a single sentence. -7- 6. The demand for a good X is given by X P P IY X = Answer the following questions. Support your assertions using algebra. a. Is good X normal? Why or why not? b. Is good X a luxury? Why or why not? c. Is good X Giffen? Why or why not? -10- Problems 1. The Kreatofagos family is having a barbecue. They send their son, Bobiras, to the local store to buy meat. The parents don’t know the prices of meat in the store. They give Bobiras $40 and tell him to spend all the money on beef and chicken, but buy twice as many pounds of beef than chicken regardless of the prices in the store. a. Do the instructions of the parents imply that beef and chicken perfect substitutes or do they imply that they are perfect complements ? Why ? b. What is the budget constraint of Bobiras as he heads into the store ? c. If the price of chicken is $2.7 per pound and the price of beef $4.0 per pound, how many pounds of each will he purchase ? d. Suppose that, on the way to the check out counter, Bobiras finds out a coupon that entitles him to 25% off on any beef. [It is today’s special!] Will Bobiras buy more beef as a result? If so, how much more ? e. Will he also buy more chicken ? If so, how much more ? 2. A consumer always consumes products X and Y in fixed proportions regardless of prices: 2 units of X are consumed with 3 units of Y. The price of X is and the price of Y is . The consumer’s income is I. a. How many units of X and how many units of Y will this consumer purchase? (The answer will be a function of prices and income.) b. In the space below, draw the Engel curve for X. Make sure you label the graph carefully, including giving the intercept and the slope of the Engel curve. -11- 3. Consider a consumer with a utility function for goods X and Y given by The price of Y is equal to 5 and the price of X is equal to 10. The consumer has income I. a. How many units of X and how many units of Y will the consumer purchase if I=5? b. How many units of X and how many units of Y will the consumer purchase if I=20? c. Derive and plot the Engel curve for good Y. Label your graph carefully. 4. A consumer always consumes soda (S) and chips (C) in fixed proportions regardless of prices: 5 ounces of S are consumed with 2 ounces of C. The price of chips is always equal to 0.2 per ounce, while the price of soda varies from time to time, as it is often on sale, and is denoted by . The consumer’s income budget for soda and chips is equal to I. a. How many units of soda (S) and how many units of chips (C) will this consumer purchase? (The answer will be a function of the price of soda and the budget for soda and chips). b. Does the consumption of chips change when soda is on sale, and if so, it what way? Can you explain in plain, clear English why the price of soda has this effect on the consumption of chips? c. In the space below, draw the relationship between the consumption of soda and the consumer’s budget for soda and chips, with I in the horizontal axis and the consumption of soda in the vertical axis. Make sure you label the graph carefully, including labeling the slope and intercept. -12- 5. Consider a consumer with a utility function for goods X and Y given by The price of Y is equal to 5 and the price of X is equal to 10. The consumer has income I. a. Draw two indifference curves for this consumer with Y on the vertical axis and X in the horizontal axis. It does not matter which two indifference curves you draw, but you must label your graph clearly. b. How many units of X and how many units of Y will the consumer purchase if I=110? c. Compute the optimal consumption of Y as a function of income I. Plot your answer in a graph with income in the horizontal axis and Y in the vertical axis. Label your graph carefully.