Suggestions for problem set 3

The main concepts pertaining to this problem set are the **relationship of the quantity demanded to price** **and income** and the notion of an **elasticity of demand**.

You need to be aware that whenever price changes, the quantity demanded will change as well. This needs to be taken into account when projecting the effect of a price increase brought about by a tax on the quantity consumed of a good, the total expenditures on the good, and the total amout of tax paid by consumers. This theme is relevant to problem 2.

A key concept in this problem set is the **price elasticity of demand**. You should be familiar with the definition of the price elasticity of demand, the formula used to compute it, and most of all what it measures. This is developed in Chapter 7 of the textbook. Problem 1 takes you through a numerical example concerning demand in which you are required to make elasticity calculations. Make sure you do all the calculations in this problem on your own, without relying on the answers in the solution set to problem set 3. This will give you some actual experience computing the price elasticity, which should give you a feel for what it measures.

The price elasticity of demand can be used in alternative ways. **It measures the percentage change in the quantity demanded of a good per percentage change in the price of the good**. For example, suppose the price elasticity of demand equals 4. This means that if the price increases by 1%, the quantity demanded falls by 4% (the quantity demanded and price always move in opposite directions). Thus, if you knew the price elasticity of demand and were given a price change, you could compute the percentage change in the quantity demanded. For example, if price increased by 2% and the price elasticity of demand equaled 3, then quantity would decline by 6%. Similarly, if you were given a percentage change in the quantity demanded and the price elasticity of demand, you could compute the percentage change in price that brought about the percentage change in the quantity demanded. Think over how you would do this. Suppose, for example, that the price elasticity of demand equaled 2 and a price change brought about a 6% increase in the quantity demanded. Solve for the percentage change in price. Use this reasoning to answer problem 3.

Another feature of the price elasticity of demand is **that it can be used to determine whether total expenditures by consumers on a good go up, down, or stay the same when price changes**. Total expenditures equal price times quantity. If price changes, quantity changes in the opposite direction, so without further information it is not possible to tell whether a price change will bring about an increase, decrease, or no change in total expenditures. You need to know how sensitive the quantity demanded is to a price change to forecast the effect of a price change on total expenditures. This is what the price elasticity of demand measures. This is developed further on pages 96-98 of the textbook. Review this material. Note that the total expenditures of consumers on a good equal the total revenues taken in by sellers of the good. Use this and how the price elasticity of demand can be used to forecast the effect of a price change on total expenditures to answer problems 4c and 4d (problems 4a and 4b can be answered using the suggestions developed above) and also problems 5a and 5c.

There are other elasticities of demand than the price elasticity of demand. Indeed, **there is an elasticity of demand for any factor that affects the quantity demanded**. A prominent factor that affects the quantity demanded is **income**. Another is the **price of other, related goods**. When income or the price of other, related goods changes, the quantity consumers demand of a good generally changes. Thus, holding the price of the good constant, when factors such as income or the price of related goods change, the quantity demanded changes. This causes a **shift in the demand curve itself**. This is different from a movement along the demand curve brought about by a change in the price of the good itself. This is developed on pages 84-85 of the textbook. Review this material. The distinction between a shift in the demand curve and a movement along the demand curve is an important one that is often confused.

There is an elasticity of demand for any factor that causes the demand curve to shift. For example, there is an **income elasticity of demand**. It measures the sensitivity of the quantity demanded to a change in income. Analogously to the price elasticity of demand, it quantifies the percentage change in the quantity demanded per one percent change in income. For example, if the income elasticity of demand equals 2, for each one percent increase in income, the quantity demanded increases by 2% (for all factors other than price, the sign of the elasticity indicates the direction of change in the quantity demanded when the factor changes—e.g., if the income elasticity of demand is positive, it indicates that when income increases, the quantity demanded increases and when income decreases, the quantity demanded decreases). Review the material on pages 100-103 in the textbook regarding elasticities other than the price elasticity of demand. Think about what these elasticities measure. Does the income elasticity of demand, for example, tell you anything about how the quantity demanded changes when the price of a good changes? Does it tell you anything about how the quantity demanded of a good changes when the income of consumers changes? when the prices of other, related goods change? Use your answers to analyze problem 5b.

Quiz 3 exploits all the themes developed on this problem set—how price changes affect the quantity demanded, and what the various elasticities measure and tell you about the effects of price and income changes on the quantity demanded and total expenditures. You need to exploit all these themes to answer all the individual questions in the quiz.