HW 2 Solutions.pdf
- 1. ECON 203 Homework #2 Solutions 1) Can a set of indifference curves be upward sloping? If so, what would this tell you about the two goods? A set of indifference curves can be upward sloping if we violate assumption number three; more is preferred to less. When a set of indifference curves is upward sloping, it means one of the goods is a “bad” so that the consumer prefers less of that good rather than more. The positive slope means that the consumer will accept more of the bad only if he also receives more of the other good in return. As we move up along the indifference curve the consumer has more of the good he likes, and also more of the good he does not like. 2) Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one can of Coke. a. What can you say about Jon’s marginal rate of substitution? Jon’s marginal rate of substitution can be defined as the number of cans of Coke he would be willing to give up in exchange for a can of Sprite. Since he is always willing to trade one for one, his MRS is equal to 1. b. Draw a set of indifference curves for Jon. Since Jon is always willing to trade one can of Coke for one can of Sprite, his indifference curves are linear with a slope of −1. 3) Janelle and Brian each plan to spend $20,000 on the styling and gas mileage features of a new car. They can each choose all styling, all gas mileage, or some combination of the two. Janelle does not care at all about styling and wants the best gas mileage possible. Brian likes both equally and wants to spend an equal amount on each. Using indifference curves and budget lines, illustrate the choice that each person will make.
- 2. ECON 203 Homework #2 Solutions Plot thousands of dollars spent on styling on the vertical axis and thousands spent on gas mileage on the horizontal axis as shown above. Janelle, on the left, has indifference curves that are vertical. If the styling is there she will take it, but she otherwise does not care about it. As her indifference curves move over to the right, she gains more gas mileage and more satisfaction. She will spend all $20,000 on gas mileage at point J. Brian, on the right, has indifference curves that are L-shaped. He will not spend more on one feature than on the other feature. He will spend $10,000 on styling and $10,000 on gas mileage. His optimal bundle is at point B. 4) Explain the difference between each of the following terms: a. a price consumption curve and a demand curve. The difference between a price consumption curve (PCC) and a demand curve is that the PCC shows the quantities of two goods that a consumer will purchase as the price of one of the goods changes, while a demand curve shows the quantity of one good that a consumer will purchase as the price of that good changes. The graph of the PCC plots the quantity of one good on the horizontal axis and the quantity of the other good on the vertical axis. The demand curve plots the quantity of the good on the horizontal axis and its price on the vertical axis. b. an individual demand curve and a market demand curve. An individual demand curve plots the quantity demanded by one person at various prices. A market demand curve is the horizontal sum of all the individual demand curves for the product. It plots the total quantity demanded by all consumers at various prices c. an Engel curve and a demand curve. An Engel curve shows the quantity of one good that will be purchased by a consumer at different income levels. The quantity of the good is plotted on the horizontal axis and the consumer’s income is on the vertical axis. A demand curve is like an Engel curve except that it shows the quantity that will be purchased at different prices instead of different income levels. d. an income effect and a substitution effect. Both the substitution effect and income effect occur because of a change in the price of a good. The substitution effect is the change in the quantity demanded of the good due to the price change, holding the consumer’s utility constant. The income effect is the change in the quantity demanded of the good due to the change in purchasing power brought about by the change in the good’s price. 5) Explain whether the following statements are true or false. a. The marginal rate of substitution diminishes as an individual moves downward along the demand curve. True. The consumer maximizes his utility by choosing the bundle on his budget line where the price ratio is equal to the MRS. For goods 1 and 2, P1/P2 = MRS. As the price of good 1 falls, the consumer moves downward along the demand curve for good 1, and the price ratio (P1/P2) becomes smaller. Therefore, MRS must also become smaller, and thus MRS diminishes as an individual moves downward along the demand curve.
- 3. ECON 203 Homework #2 Solutions b. The level of utility increases as an individual moves downward along the demand curve. True. As the price of a good falls, the budget line pivots outward, and the consumer is able to move to a higher indifference curve. c. Engel curves always slope upwards. False. If the good is inferior, then as income increases, quantity demanded decreases, and therefore the Engel curve slopes downwards. 6) Suppose that a consumer spends a fixed amount of income per month on the following pairs of goods: a. tortilla chips and salsa b. tortilla chips and potato chips c. movie tickets and gourmet coffee d. travel by bus and travel by subway If the price of one of the goods increases, explain the effect on the quantity demanded of each of the goods. In each pair, which are likely to be complements and which are likely to be substitutes? a. If the price of tortilla chips increases, the consumer will demand fewer tortilla chips. Since tortilla chips and salsa are complements, the demand curve for salsa will decrease (shift to the left), and the consumer will demand less salsa. b. If the price of tortilla chips increases, the consumer will demand fewer tortilla chips. Since tortilla chips and potato chips are substitutes, the demand for potato chips will increase (the demand curve will shift to the right), and the consumer will demand more potato chips. c. The consumer will demand fewer movies after the price increase. You might think the demands for movies and gourmet coffee would be independent of each other. However, because the consumer spends a fixed amount on the two, the demand for coffee will depend on whether the consumer spends more or less of her fixed budget on movies after the price increase. If the consumer’s demand elasticity for movie tickets is elastic, she will spend less on movies and, therefore, more of her fixed income will be available to spend on coffee. In this case, her demand for coffee increases, and she buys more gourmet coffee. The goods are substitutes in this situation. If her demand for movies is inelastic, however, she will spend more on movies after the price increase and, therefore, less on coffee. In this case, she will buy less of both goods in response to the price increase for movies, so the goods are complements. Finally, if her demand for movies is unit elastic, she will spend the same amount on movies and therefore will not change her spending on coffee. In this case, the goods are unrelated, and the demand curve for coffee is unchanged. d. If the price of bus travel increases, the amount of bus travel demanded will fall, and the demand for subway rides will rise, because travel by bus and subway are substitutes. The demand curve for subway rides will shift to the right.
- 4. ECON 203 Homework #2 Solutions 7) Explain the difference between a positive and a negative network externality and give an example of each. A positive network externality exists if one individual’s demand increases in response to the purchase of the good by other consumers. Fads are an example of a positive network externality. For example, each individual’s demand for baggy pants increases as more other individuals begin to wear baggy pants. This is also called a bandwagon effect. Another example of a positive network externality occurs with communications equipment such as telephones. A telephone is more desirable when there are a large number of other phone owners to whom one can talk. A negative network externality exists if the quantity demanded by one individual decreases in response to the purchase of the good by other consumers. In this case the individual prefers to be different from other individuals. As more people adopt a particular style or purchase a particular type of good, this individual will reduce his demand for the good. Goods like designer clothing can have negative network externalities, as some people would not want to wear the same clothes that many other people are wearing. This is also known as the snob effect. Another example of a negative network externality is road congestion. As more people use a road, the more congested it becomes, and the less valuable it is to each driver. Some people will drive on the road less often (i.e., demand less road services) when it becomes overly congested. 8) Each week, Bill, Mary, and Jane select the quantity of two goods, X1 and X2, that they will consume in order to maximize their respective utilities. They each spend their entire weekly income on these two goods. a. Suppose you are given the following information about the choices that Bill makes over a three- week period: Did Bill’s utility increase or decrease between week 1 and week 2? Between week 1 and week 3? Explain using a graph to support your answer. Bill’s utility fell between weeks 1 and 2 because he consumed less of both goods in week 2. Between weeks 1 and 2 the price of good 1 rose and his income remained constant. The budget line pivoted inward and he moved from U1 to a lower indifference curve, U2, as shown in the diagram. Between week 1 and week 3 his utility rose. The increase in income more than compensated him for the rise in the price of good 1. Since the price of good 1 rose by $1, he would need an extra $10 to afford the same bundle of goods he chose in week 1. This can be found by multiplying week 1 quantities times week 2 prices. However, his income went up by $15, so his budget line shifted out beyond his week 1 bundle. Therefore, his original bundle lies within his new budget set as shown in the diagram, and his new week 3 bundle is on the higher indifference curve U3.
- 5. ECON 203 Homework #2 Solutions 9) The ACME Corporation determines that at current prices the demand for its computer chips has a price elasticity of –2 in the short run, while the price elasticity for its disk drives is –1. a. If the corporation decides to raise the price of both products by 10 percent, what will happen to its sales? To its sales revenue? We know the formula for the elasticity of demand is EP = %∆Q/%∆P. For computer chips, EP = –2, so –2 = %∆Q/10, and therefore %∆Q = –20. Thus a 10 percent increase in price will reduce the quantity sold by 20 percent. For disk drives, EP = –1, so a 10 percent increase in price will reduce sales by 10 percent. Sales revenue will decrease for computer chips because demand is elastic and price has increased. Sales revenue for disk drives will remain unchanged because demand elasticity is –1. b. Can you tell from the available information which product will generate the most revenue? If yes, why? If not, what additional information do you need? No. Although we know the elasticity of demand, we do not know the prices or quantities sold, so we cannot calculate the revenue for either product. We need to know the prices of chips and disk drives and how many of each ACME sells. 10) You run a small business and would like to predict what will happen to the quantity demanded for your product if you raise your price. While you do not know the exact demand curve for your product, you do know that in the first year you charged $45 and sold 1200 units and that in the second year you charged $30 and sold 1800 units. a. If you plan to raise your price by 10 percent, what would be a reasonable estimate of what will happen to quantity demanded in percentage terms? We must first find the price elasticity of demand. Because the price and quantity changes are large in percentage terms, it is best to use the arc elasticity measure. EP = (∆Q/∆P)(average P/average Q) = (600/–15)(37.50/1500) = –1. With an elasticity of –1, a 10 percent increase in price will lead to a 10 percent decrease in quantity.
- 6. ECON 203 Homework #2 Solutions a. If you raise your price by 10 percent, will revenue increase or decrease? When elasticity is –1, revenue will remain constant if price is increased.