Consumers and Incentives in Economics

Jason Moore

Here are my notes and thoughts on consumers and incentives in economics.

The buyer’s problem has three parts: what you like, prices, and your budget. An optimizing buyer makes decisions at the margin. An individual’s demand curve reflects an ability and willingness to pay for a good or service. Consumer surplus is the difference between what a buyer is willing to pay for a good and what the buyer actually pays. Elasticity measures a variable’s responsiveness to changes in another variable.

 

First, as a buyer, you want to buy goods and services that you like, because you prefer to buy what tastes good, sounds good, or looks good. You must also consider prices of the various goods and services that interest you. 

 

The benefits that you receive from consuming goods and services are a direct result of your tastes and preferences. When it comes to the buyer’s problem, economists assume that the consumer attempts to maximize the benefits from consumption. 

 

Prices are the most important incentives that economists study. They allow us to formally define the relative cost of goods. 

 

The final ingredient of the buyer’s problem is what you can buy. The budget set is the set of all possible bundles of goods and services that a consumer can purchase with his income. 

 

An optimizing buyer makes decisions at the margin. 

 

A decrease in the price of either good will cause the budget constraint to pivot outward. When a price changes, the opportunity cost changes. This will cause the buyer to change the optimal quantities consumed. 

 

With an understanding of how to spend optimally, we can begin to construct demand curves. An individual’s willingness to pay measured over different quantities of the same good makes up the individual’s demand curve. The demand curve isolates the contribution that a good’s own price makes toward determining the quantity demanded in a given time period.

 

The quantity demanded refers to the amount of a good that buyers are willing to purchase at a particular price. A demand curve maps how quantity demanded responds to price changes. 

 

The demand curve shows how the quantity demanded depends on the price of the good. The demand curve is downward sloping. Every point on your demand curve represents a unique price and quantity level. 

 

We have learned we should recognize the incentives that we face and make decisions based on marginal analysis. That is, we should consider the marginal benefits and marginal costs in our decision making. In markets, the process of optimal decision making by consumers often yields total benefits well above the price we pay for goods. Economists give these market-created benefits a name, consumer-surplus. Consumer surplus is the difference between the willingness to pay and the price paid for the good. 

 

When price increases, consumer surplus decreases. The higher the price, the smaller the difference between the willingness to pay and the market price. Furthermore, the higher the price, the lower the quantity demanded. 

 

If we want to know how responsive quantity demanded is to a change in price, we want to know about price elasticity. Elasticity measures the sensitivity of one economic variable to a change in another. In other words, it tells us how much one variable changes when another variable changes. More precisely, elasticity is a ratio of percentage changes in variables. 

 

Elasticity is an important concept because it takes into account not only the direction of change but also the size of the change. The different types are:

  1. Price elasticity of demand
  2. Cross-price elasticity of demand
  3. Income elasticity of demand

 

We know from the law of demand that when the price of a good increases, the quantity demanded generally falls. However, we do not know how much quantity demanded falls. The price elasticity of demand measures the percentage change in quantity demanded of a good resulting from a percentage change in the good’s price. 

 

The distinction between whether a good has a price elasticity of demand greater than or less than 1 is very important. A price elasticity of 1 says that if the price is increased by 20% then quantity demanded decreases by 20%. 20/20=1. So, if price elasticity is greater than 1, price increases hurt revenue.

 

Elasticity is much different than the slope of a line. Even though the slope is the same over the entire demand curve, the elasticity varies over the slope of the line. This is because the ratio of price to quantity changes as we move along the demand curve. 

 

Next, elasticities tend to vary over ranges of the demand curve. They are different at the top, middle, and bottom of the curve. 

 

Another measure that economists often calculate is arc elasticity. The arc elasticity achieves a stable elasticity regardless of the starting point by using the average price and quantity in the calculation. 

 

Goods with a price elasticity of demand greater than 1 have elastic demand. The percentage change in quantity demanded is greater than the percentage change in price. Peanut butter is an example.

 

Goods with a price elasticity of demand equal to 1 have unit elastic demand. 1 percent price change affects quantity demanded by 1 percent. So, in this example, a price increase does not affect revenue. Wine is a good with this characteristic. 

 

Goods with a price elasticity of demand less than 1 have inelastic demand. When the price elasticity of demand is less than 1, the percentage change in quantity demanded is less than the percentage change in price. Cigarettes are such a good. 

 

Demand can also be perfectly inelastic, which means that quantity demanded is completely unaffected by price. An example of this is insulin, you just have to have it. 

 

Economists have pinpointed three primary reasons for elasticity differences:

  1. Closeness of substitutes
  2. Budget share spent on the good
  3. Available time to adjust

 

Economists are interested in much more than merely how changes in a good’s price affect consumers. Another type of inelasticity that economists consider is how quantity demanded for one good changes when the price of a substitute or complement good changes. This is called the cross-price elasticity of demand. It is a measurement of the percentage change in quantity demanded of a good due to a percentage change in another good’s price. 

 

If a cross-price elasticity is negative, then the two goods are complements. Two goods are complements when the fall in the price of one leads to a right shift in the demand curve for another. 

 

If a cross-price elasticity is positive, then the two goods are substitutes. Two goods are substitutes when the rise in the price of one leads to a right shift in the demand curve for the other. 

 

A third type of elasticity measurement has to do with how changes in income affect consumption patterns. The income elasticity of demand informs us of the percentage change in quantity demanded of a good due to a percentage change in the consumer’s income. 

 

A good is normal if the quantity demanded is directly related to income. When income rises, consumers buy more of a normal good.

 

A good is inferior if the quantity demanded is inversely related to income. When income rises, consumers buy less of an inferior good. 

 

Which of the following are necessary ingredients to the buyer’s problem?

  1. Prices of goods and services
  2. Amount of money the consumer has to spend
  3. Consumers tastes and preferences




Akio consumes two goods, books and video games. His income is $40, the price of a video game is $8 and the price of a book is $4.

Suppose Akio’s parents give him $24 for his birthday. 

Use his income, the monetary gift from his parents, and the price data to find the maximum amounts of each good that he could purchase. These will give you the endpoints of the budget constraint, from which you can sketch the budget set. 

  1. 8 video games
  2. 16 books



Now suppose Akio’s parents had given him three video games for his birthday instead of giving him $24. Akio is a very polite young man and would never return a gift that his parents had given him for cash.

The budget constraint is simply a subset of the budget set; graphically, it is the outer edge of the budget set that separates affordable bundles from unaffordable bundles. 

 

Based on your preceding answers, which of the following applies:

  1. He could be indifferent between a gift of $24 and a gift of three video games.
  2. Akio could prefer a gift of three video games.

 

Hanna has $420 to spend on movies and concerts. Suppose the price of a movie ticket is $14 and the price of a concert ticket is $70.

  1. 30 movie tickets
  2. 6 concert tickets

 

Suppose the price of concert tickets drops to $60.

  1. 30 movie tickets
  2. 7 concert tickets

 

Now suppose Hanna has $840 to spend rather than 4420. How will this change affect hann’s budget line?

  1. It shifts outward in a parallel fashion

 

Given the information about Hanna’s income and the prices for concerts and movies, we are unable to determine where on the budget line hanna would choose to consume because:

  1. Hanna’s tastes regarding movies and concerts are unknown to us

 

Charley spends all of his income on soft drinks and pizza. Suppose he is currently buying these products in amounts such that his marginal benefit from an additional soft drink is $180 and his marginal benefit from an additional slice of pizza is $80. If the price of a soft drink is $4 and the price of a slice of pizza is $3, is Charley maximizing his total benefits?

  1. No, he should shift consumption toward soft drinks and away from pizza to maximize his total benefits.

 

The demand curve shows:

  1. How the quantity demanded responds to changes in the price of the good

 

Everything else the same, as the price of the good increases, quantity demanded:

  1. Decreases



According to economists, the process of optimal decision making by consumers typically yields total benefits well above the amount paid for the goods. 

These market-created benefits are referred to as:

  1. Consumer surplus

Using the graph to the right, they are represented by area:

  1. B

Suppose now that the market price falls. According to the graph, the excess of total benefits over the total amount spent by consumers will:

  1. Increase



The price of rice in a small country is currently $9 per pound. In order to help low-income people afford an adequate diet, the government introduces a subsidy of $3 per pound of rice. Using the graph on the right, show the area representing the increase in consumer surplus as a result of the subsidy. Assume that the full amount of the subsidy is passed to consumers. To do this, you must create a single area by combining two shapes, rectangle and triangle

The formula for the area of a triangle is:

  1. Base * height

The formula for the area of a triangle is:

  1. (base*height)*½

The sum of these will measure the increase in consumer surplus:

  1. (60) + 15=75

 

Now using the rectangle drawing tool, show the cost of the subsidy in the graph to the right. The hatched area measures the increase in consumer surplus derived above.

According to the graph, the cost of the subsidy is:

The cost of the subsidy is the per unit subsidy*the number of units consumed after the subsidy takes effect.

  1. 30*3=90

From the analysis, the cost of the subsidy(90) exceeds the increase in consumer surplus(75) by $15

 

The price elasticity of demand shows the percentage change in the quantity demanded of a good due to

  1. A percentage change in the good’s price

In the market for sneakers, suppose Green’s price elasticity of demand is 0.2, smith’s price elasticity is 1.2, and the price elasticity of all the other consumers is greater than 0.2 but less than 1.2. Could the market price elasticity be less than 0.2 or greater than 1.2?

  1. No, it must be between 0.2 and 1.2

 

Which of the following shows the arc elasticity method of calculating the price elasticity of demand?

  1. \( \frac{\frac{Q_2-Q_1}{(Q_2+Q_1)/2}}{\frac{P_2-P_1}{(P_2+P_1)/2}}}

 

Consider the following statement: given that bacon and eggs are complementary good, if the price of eggs decreases the demand for both goods will rise. Is this an accurate statement?

  1. It is somewhat inaccurate. The decrease in the price of eggs will increase the quantity demanded for eggs. It will, however, as the statement claims, increase the demand for bacon.

 

Consider the following demand schedule for bags.

13 60

15 56

17 48

The price elasticity of demand measures the percentage change in quantity demanded of a good resulting from a percentage change in the good’s price.

Using the midpoint formula:

Percentage change in price= \( \frac{(15-13)}{(15+13)/2}=14.3 \) percent

Percentage change in quantity = \( \frac{(56-60)}{(56+60)/2} = -6.9 \) percent

Price elasticity of demand = \( \frac{-6.9}{14.3} = -0.5 \) 

When the price of bags rises from 13 to 15, the price elasticity of demand is approximately:

  1. -0.5

When the price of bags increases from 15 to 17, the total expenditure will:

  1. Decrease

Because the price elasticity of demand is:

  1. Relatively elastic

 

Jonathan works at a convenience store and makes note of changes to sales after the price of liquid soap unexpectedly increases by 15%. He notices that the sale of shampoo decreases by 3 percent and the sale of lotion increases by 10 percent. 

The cross-price elasticity of demand is a measurement of the percentage change in quantity demanded of a good due to a percentage change in the price of another good.

The cross-price elasticity between liquid soap and shampoo is negative.

(-3 percent / 15 percent) = -0.2

The cross-price elasticity of demand between liquid soap and shampoo is:

  1. -0.2

Based on the cross-price elasticity of demand, we can infer that liquid soap and lotion are substitutes

 

Three years after graduating from college, you get a promotion and a 12 percent raise. Your consumption habits change accordingly. Suppose your consumption of frozen hot dogs has reduced by 4 percent.

The income elasticity of demand is the percentage change in quantity demanded of a good due to an increase in the consumer’s income.  

In the given scenario, the income elasticity of demand is:

\( \frac{-4 \text{percent}}{12 \text{percent}} = -0.33 \)

Your income elasticity of demand is:

  1. -0.33

Thus, we can say that a frozen hot dog is an inferior good

Suppose your consumption of pork chops has increased by 8 percent. Your income elasticity of demand is:

  1. 8/12=.67

Thus, we can say that a pork chop is a normal good

Suppose your consumption of sockeye salmon has increased by 20 percent. Your income elasticity of demand is:

  1. 20/12=1.67

Thus we can say that sockeye salmon is a:

  1. Luxury good



Suppose that Hershey’s increases the price of its chocolate ice cream syrup by 15 percent. In response, the quantity demanded of Nesquik chocolate syrup rises by 11 percent and the quantity demanded of Breyer’s vanilla ice cream falls by 5 percent.

The cross-price elasticity of demand measures the percentage change in quantity demanded of a good due to a percentage change in another good’s price.

If a cross-price elasticity is negative, then the two goods are complements. Alternatively, if a cross-price elasticity is positive, then the two goods are substitutes.

The cross-price elasticity of demand between Hershey’s syrup and nequik’s syrup is:

  1. Positive

Implying these two goods are:

  1. Substitutes

 

The cross-price elasticity of demand between Hershey’s syrup and Breyer’s ice cream is:

  1. Negative

Implying these two goods are:

  1.  complements

Suppose that incomes rise by 9 percent given the price change cited above. As a result, Hershey’s experiences a 5 percent increase in sales volume. Given this information, hershey’s syrup is a:

  1. Normal good

 

For this exercise, assume there are only two goods. 

The substitution effect of a decrease in the price of one good always:

  1. decreases

The amount of that good in the individual’s new consumption choice and:

  1. Increases the amount of the other good

The associated income effect of a decrease in the price of one good:

  1. Will always decrease the quantity of that good and:
  2. Will always decrease the quantity of the other good, but the

Quantities of the two goods in the new consumption choice cannot simultaneously:

  1. Increase as a result of the income effect

 

If an individual only consumes goods x and y and is currently maximizing her total benefits, which of the following must be true?

  1. All of the above
  2. The equal bang for the buck rule is adhered to
  3. mbx/px = mby/py
  4. The marginal benefits per dollar spent are the same for both good
  5. No other consumption choice can make total benefits greater



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