Complementary Good or Substitute Good | Which of the following combinations of goods are complements and which are substitutes?

Which of the following combinations of goods are complements and which are substitutes?
Can they be either in different circumstances? Discuss.

a.  a mathematics class and an economics class

b.  tennis balls and a tennis racket

c.  steak and lobster

d.  a plane trip and a train trip to the same destination

e.  bacon and eggs

ANSWER  

a.  a mathematics class and an economics class

If the math class and the economics class do not conflict in scheduling, then the classes could be either complements or substitutes. Math is important for understanding economics, and economics can motivate mathematics, so the classes could be complements. If the classes conflict or the student has room for only one in his schedule, they are substitutes.

b.  tennis balls and a tennis racket

Tennis balls and a tennis racket are both needed to play tennis, thus they are complements.

c.  steak and lobster

Foods can both complement and substitute for each other. Steak and lobster can be substitutes, as when they are listed as separate items on a menu. However, they can also function as complements because they are often served together.

d.  a plane trip and a train trip to the same destination

Two modes of transportation between the same two points are substitutes for one another.

e.  bacon and eggs

Bacon and eggs are often eaten together and are complementary goods in that case. However, in relation to something else, such as pancakes, bacon and eggs can function as substitutes.

Indifference Curve | Explain why two indifference curves cannot intersect.

Explain why two indifference curves cannot intersect.

ANSWER

The figure below shows two indifference curves intersecting at point A. We know from the definition of an indifference curve that the consumer has the same level of utility for every bundle of goods that lies on the given curve. In this case, the consumer is indifferent between bundles A and B because they both lie on indifference curve U₁. Similarly, the consumer is indifferent between bundles A and C because they both lie on indifference curve U₂. By the transitivity of preferences this consumer should also be indifferent between C and B. However, we see from the graph that C lies above B, so C must be preferred to B because C contains more of Good Y and the same amount of Good X as does B, and more is preferred to less. But this violates transitivity, so indifference curves must not intersect.

Individual Preference | What are the four basic assumptions about individual preferences?

What are the four basic assumptions about individual preferences? 

Explain the significance or meaning of each.

ANSWER

(1) Preferences are complete: this means that the consumer is able to compare and rank all possible baskets of goods and services. 

(2) Preferences are transitive: this means that preferences are consistent, in the sense that if bundle A is preferred to bundle B and bundle B is preferred to bundle C, then bundle A is preferred to bundle C. 

(3) More is preferred to less: this means that all goods are desirable, and that the consumer always prefers to have more of each good. 

(4) Diminishing marginal rate of substitution: this means that indifference curves are convex, and that the slope of the indifference curve increases (becomes less negative) as we move down along the curve. As a consumer moves down along her indifference curve she is willing to give up fewer units of the good on the vertical axis in exchange for one more unit of the good on the horizontal axis. This assumption also means that balanced market baskets are generally preferred to baskets that have a lot of one good and very little of the other good.

Supply & Demand | Exercise on rent control agency of New York City

The rent control agency of New York City has found that aggregate demand is QD = 160 - 8P. 

Quantity is measured in tens of thousands of apartments. 

Price, the average monthly rental rate, is measured in hundreds of dollars. 

The agency also noted that the increase in Q at lower P results from more three-person families coming into the city from Long Island and demanding apartments. 

The city’s board of realtors acknowledges that this is a good demand estimate and has shown that supply is QS = 70 + 7P.

a.       If both the agency and the board are right about demand and supply, what is the free-market price? What is the change in city population if the agency sets a maximum average monthly rent of $300 and all those who cannot find an apartment leave the city?

b.      Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a “fair” rate of return. If 50% of any long-run increases in apartment offerings come from new construction, how many apartments are constructed?

ANSWER

a.       If both the agency and the board are right about demand and supply, what is the free-market price? What is the change in city population if the agency sets a maximum average monthly rent of $300 and all those who cannot find an apartment leave the city?

Set supply equal to demand to find the free-market price for apartments:

160 - 8P = 70 + 7P, or P = 6,

which means the rental price is $600 since price is measured in hundreds of dollars. Substituting the equilibrium price into either the demand or supply equation to determine the equilibrium quantity:

QD = 160 - 8(6) = 112

and

QS = 70 + 7(6) = 112.

The quantity of apartments rented is 1,120,000 since Q is measured in tens of thousands of apartments. If the rent control agency sets the rental rate at $300, the quantity supplied would be 910,000 (QS = 70 + 7(3) = 91), a decrease of 210,000 apartments from the free-market equilibrium.

Assuming three people per family per apartment, this would imply a loss in city population of 630,000 people. Note: At the $300 rental rate, the demand for apartments is 1,360,000 units, and the resulting shortage is 450,000 units (1,360,000 - 910,000).

However, excess demand (the shortage) and lower quantity demanded are not the same concept. The shortage of 450,000 units is the difference between the number of apartments demanded at the new lower price (including the number demanded by new people who would have moved into the city), and the number supplied at the lower price. But these new people will not actually move into the city because the apartments are not available.

Therefore, the city population will fall by 630,000, which is due to the drop in the number of apartments available from 1,120,000 (the old equilibrium value) to 910,000.

b.      Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a “fair” rate of return. If 50% of any long-run increases in apartment offerings come from new construction, how many apartments are constructed?

At a rental rate of $900, the demand for apartments would be 160 - 8(9) = 88, or 880,000 units, which is 240,000 fewer apartments than the original free-market equilibrium number of 1,120,000. Therefore, no new apartments would be constructed.

Supply & Demand | Find Market-Clearing Price & Quantity

Suppose the demand curve for a product is given by Q = 300 - 2P + 4I, where I is average income measured in thousands of dollars. The supply curve is Q = 3P - 50.

a.      If I = 25, find the market-clearing price and quantity for the product.

b.      If I = 50, find the market-clearing price and quantity for the product.

c.       Draw a graph to illustrate your answers.

ANSWER

a. If I = 25, find the market-clearing price and quantity for the product.

Given I = 25, the demand curve becomes Q = 300 − 2P + 4(25), or Q = 400 − 2P.  Set demand equal to supply and solve for P and then Q:

400 - 2P = 3P - 50

P = 90

Q = 400 - 2(90) = 220

b. If I = 50, find the market-clearing price and quantity for the product.

Given I = 50, the demand curve becomes Q = 300 - 2P + 4(50), or Q = 500 - 2P. Setting demand equal to supply, solve for P and then Q:

500 - 2P = 3P - 50

P = 110

Q = 500 - 2(110) = 280

c. Draw a graph to illustrate your answers.

It is easier to draw the demand and supply curves if you first solve for the inverse demand and supply functions, i.e., solve the functions for P. Demand in part a is P = 200 - 0.5Q and supply is P = 16.67 + 0.333Q. These are shown on the graph as Da and S. Equilibrium price and quantity are found at the intersection of these demand and supply curves. When the income level increases in part b, the demand curve shifts up and to the right. Inverse demand is P = 250 - 0.5Q and is labeled Db. The intersection of the new demand curve and original supply curve is the new equilibrium point.

Supply & Demand | True or False

Are the following statements true or false? Explain your answers.

a. The elasticity of demand is the same as the slope of the demand curve.

b. The cross-price elasticity will always be positive.

c. The supply of apartments is more inelastic in the short run than the long run.

a.      The elasticity of demand is the same as the slope of the demand curve.

False. Elasticity of demand is the percentage change in quantity demanded divided by the percentage change in the price of the product. In contrast, the slope of the demand curve is the change in quantity demanded (in units) divided by the change in price (typically in dollars).

The difference is that elasticity uses percentage changes while the slope is based on changes in the number of units and number of dollars.

b.      The cross-price elasticity will always be positive.

False. The cross-price elasticity measures the percentage change in the quantity demanded of one good due to a 1% change in the price of another good. This elasticity will be positive for substitutes (an increase in the price of hot dogs is likely to cause an increase in the quantity demanded of hamburgers) and negative for complements (an increase in the price of hot dogs is likely to cause a decrease in the quantity demanded of hot dog buns).

c.       The supply of apartments is more inelastic in the short run than the long run.

True. In the short run it is difficult to change the supply of apartments in response to a change in price. Increasing the supply requires constructing new apartment buildings, which can take a year or more. Therefore, the elasticity of supply is more inelastic in the short run than in the long run.

Supply & Demand | Explain the difference between a shift in the supply curve and a movement along the supply curve.

Explain the difference between a shift in the supply curve and a movement along the supply curve.

ANSWER

A movement along the supply curve occurs when the price of the good changes. A shift of the supply curve is caused by a change in something other than the good’s price that results in a change in the quantity supplied at the current price. Some examples are a change in the price of an input, a change in technology that reduces the cost of production, and an increase in the number of firms supplying the product.