ECON 211 Problems, Spring 2008

Exercise 1: John has a weekly allowance of $240.00 to spend on pizza, cinema visits, and video rentals. The following table shows the marginal utility (MU) derived from the consumption of the three goods: Qpizza MU Qcinema MU Qvideo MU 1 50 1 25 1 15 2 20 2 20 2 12 3 18 3 15 3 10 4 16 4 12 4 9 5 14 5 10 5 8 6 12 6 8 6 7 7 9 7 6 7 6 8 7 8 5 8 5 9 6 9 4 9 4 10 4 10 3 10 3 11 2 11 2 11 2 12 1 12 1 12 1 13 0 13 0 13 0 If the price of pizza is $20, the price of cinema tickets is $10 and the price of video rentals is $5; 1. Determine the utility maximization choice of John. 2. Determine the total utility that John will get from his choice made in 1. Exercise 2: You have $100 to spend on movies and compact discs. Movies are priced at $5 each and CDs at $20 each. 1. Draw the budget line labelling the axes and calculating the necessary numbers. 2. Place the following combinations of the two goods on the diagram above and explain each situation  12 movies and 2 CDs (combination A)  14 movies and 3 CDs (combination B)  10 movies and 2 CDs (combination C) 3. Starting from the original budget line, draw another budget line if the price of movies increased to $10 and the price of CDs decreased to $5. Exercise 3: As school increasingly stresses you out, you decide to take a couple of days off and to head for the beach for a real sun and fun deal. Since you want to look great at the beach and at the night clubs that you plan to visit extensively, you decide to buy some new outfits for the beach (B) and some elegant clothes (E) for the nightlife. Qty. Beach Wear (B) Elegant Wear (E) 1 1. Draw the total and marginal utility functions for B and E. 2. If you have a budget of USD 160 and an item of each beach and elegant wear costs USD 20, how many items of beach wear and elegant wear will you buy? Why would you not buy five items of elegant wear and three items of beach wear? How big is your consumer surplus for beach and elegant wear, respectively? 3. If you have a budget of USD 160 and an item of beach wear costs USD 20 and an item of elegant wear costs USD 40, how many items of beach wear and how many items of elegant wear would you buy? Why would you not buy three items of elegant wear and two items of beach wear? How big is your consumer surplus for beach and elegant wear, respectively? 4. Locate the price-demand combination for elegant wear in a diagram. Estimate the shape of the demand curve for elegant wear for all prices. 5. Now assume that you and two of your best friends, who have exactly the same budget and preferences like you, join you to the beach. Locate the combined price-demand combinations of you three for elegant wear in a diagram. Estimate the shape of the aggregate demand curve for elegant wear for all prices. Sketch the area that represents consumer surplus. 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Total Utility Q 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Marginal Utility Q to Q4 and Q5: Total Utility (B) Marginal Utility (B) Total Utility (E) Marginal Utility (E) 1 250 350 2 450 550 3 600 700 4 700 800 5 775 875 6 800 900 2 1 2 3 4 1 2 3 4 5 6 Q 1 2 3 4 3 6 9 12 15 18 Q Individual Aggregate The numbers on the y-Axis are in 100s Exercise 4: The following diagram represents the U.S. market for oil. 1. Use the total revenue test (on all oil sold) to determine elasticity of demand with a price drop from $18 to $16. Revenue at P = $18, R = 18 x 140 = 2520 Revenue at P = $16, R = 16 x 160 = 2560 As price falls from $18 to $16, revenue rises. Therefore demand is elastic. 3 2. Use the midpoint formula to calculate the price elasticity of demand between $18 and $16. By using the midpoint formula, we calculate an elastic demand. (20/150 -2/17) = (1/15 1/17) = 1.133. Exercise 5: Assume the following information on the price of small-screen televisions and quantity demanded. 1. Plot the demand curve. 2. Compute the price elasticity of demand between $280 and $240. 4 3. Compute the price elasticity of demand between $200 and $160. 4. Compare and discuss the two elasticity estimates computed above. Without doing any more calculations what would you expect to happen to the value of the elasticity estimates as price continues to fall? Assume a linear demand curve. Elasticity is greater for the higher prices. As price continues to fall we would expect that the elasticity would fall as well. 5. Why are elasticities of demand rather than slopes used to measure and compare responsiveness? Elasticities are useful because they are unitless, and one can therefore compare elasticities between different types of goods. In contrast, slopes are not unitless. Hence, comparison between different products is much easier with elasticity. Exercise 6: Comment on the following statement: "Elasticity is constant along a straight-line demand curve". The statement is false. While the slope is constant along a straight line, the elasticity is not. In fact, at high prices (the upper area of a demand curve) the demand is elastic. As price falls (and quantity demanded increases), the price elasticity of demand gets smaller (in absolute value). 5 Exercise 7: The demand for tobacco is price inelastic. Suppose there is a drought that destroys a large portion of the tobacco crop. What will happen in the market for tobacco? Will the equilibrium price and quantity change? If so, how? What will happen to the total revenue earned by tobacco farmers? The drought will lower the supply of tobacco. The supply of tobacco will shift to the left, increasing price but lowering the equilibrium quantity sold. However, since the demand for tobacco is price inelastic, the percentage increase in price will be larger than the percentage decrease in quantity demanded. Therefore, the total revenue earned by tobacco farmers will rise. Exercise 8: When the price of a bagel rises from $0.45 to $0.65, the quantity of cream cheese demanded falls from 12,000 to 10,000 ounces per year. Use the midpoint formula to calculate the cross-price elasticity between bagels and cream cheese. What does the sign imply about the relationship between these two goods? percentage change in quantity of cream cheese demanded = (10,000- 12,000)/11,000 = -2,000/11,000 = -18.2. percentage change in the price of a bagel = ($0.65 - $0.45)/$0.55 = 0.20/0.55 = 36.4. Therefore, the cross price elasticity = -18.2/36.4 = -0.5. Because the cross-price elasticity is negative, this implies that the two goods are complements. Exercise 9: The cross-price elasticity between X and Y is positive. Illustrate on two graphs, one for good X and one for good Y, what will happen if the supply of X decreases. 6 If the supply of X decreases, the price of X will increase, the demand curve for good Y will shift to the right, and the amount of Y purchased will increase. Exercise 10: Draw a supply curve that has a zero elasticity of supply. What might be an example of a good with a zero elasticity of supply? The supply curve will be a vertical line. Agricultural products after they have been harvested or land are examples. Exercise 11: Suppose that Jeanna's income rises. If tomatoes are a normal good, what will happen to the quantity of tomatoes purchased by Jeanna? Is this an income effect, a substitution effect, or both? Explain. Jeanna will purchase more tomatoes if her income rises because tomatoes are a normal good. This is an income effect. Her income has increased, so she is better off. There is no substitution effect in this case because there is no change in relative prices. Exercise 12: When the price of corn increases, the quantity of corn demanded falls. Explain this change in terms of income and substitution effects. When the price of corn rises, households have less purchasing power than before. If corn is a normal good, this means that they will consume less of it. This is the income effect. Also, an increase in the price of corn makes corn relatively more expensive. Thus, households will shift away from purchasing corn to purchase relatively cheaper goods. This is the substitution effect. Both effects imply that the quantity of corn demanded will fall as the price of corn rises. 7 Exercise 13: Suppose that macaroni and cheese is an inferior good and the price of macaroni and cheese rises. Explain the income and substitution effects of this price change. When the price of macaroni and cheese rises, we have less purchasing power than before. If macaroni and cheese is an inferior good, this means that we will consume more of it. This is the income effect. Also, an increase in the price of macaroni and cheese makes it relatively more expensive. Thus, households will shift away from purchasing macaroni and cheese to purchase relatively cheaper goods. This is the substitution effect. Because these two effects work in opposite directions, the outcome (in terms of the quantity of macaroni and cheese demanded) will depend on which effect is larger. While it is theoretically possible, it is unlikely for this income effect to be larger than the substitution effect. Exercise 14: Explain how income and substitution effects alter the saving behavior of households. When the interest rate rises, the opportunity cost of spending income rises and therefore, individuals will be more likely to save. This is the substitution effect. However, because the interest rate increase makes households better off, they want to purchase more normal goods and save less. This is the income effect. Exercise 15: Refer to the figure below. What can we say about the relative sizes of the income and substitution effects? 8 suppl y wage Because an increase in the wage leads to a decrease in the quantity of labor supplied, we can tell that the income effect is larger than the substitution effect. Exercise 16: Empirical evidence suggests that saving tends to rise when there is an increase in interest rates. What does this imply about the relative sizes of the income and substitution effects? Explain. The substitution effect must be larger. The substitution effect of an interest rate increase suggests that households will save more because the opportunity cost of spending has increased. The income effect suggests that an increase in the interest rate makes households better off and therefore they will want to spend more. Because saving rises when the interest rate increases, the substitution effect must be larger. 9 Quantity of labor