Demand Analysis: Quantity & Demand Function

• Demand analysis
• Quantity demanded is the amount of a good or service consumers are willing and able to purchase during a given period.
• Demand relations consist of the general demand function, the direct demand function, and the inverse demand function.

General Demand Function

• It represents the relation between quantity demanded and the six factors that affect quantity demanded.
• The quantity demanded of the good or service = Q₁ = f(P, M, PR, T, PE, N).
• "f" means "is a function of" or "depends on," and variables are defined individually below.
• P = price of the good or service
• M = consumers' income (generally per capita)
• PR = price of related goods or services
• T= taste patterns of consumers
• PE = expected price of the good in some future period
• N = number of consumers in the market

Price

• Consumers are willing and able to buy more of a good, the lower the price.
• Consumers tend to buy less of a good, the higher the price.
• Price and quantity demanded are negatively (inversely) related
• The price of a good rises, consumers shift from that good to other goods that are now relatively cheaper.
• The price of a good falls, consumers tend to purchase more of that good and less of other goods that are now relatively more expensive.

Income

• Holding constant the rest of the variables that influence consumers.
• An increase in income can cause the amount of a commodity consumers purchase either to increase or to decrease.
• A normal Good is a good or service for which an increase in income causes consumers to demand more of the good, holding all other variables in the general demand function constant.
• An Inferior Good is a good or service for which an increase in income causes consumers to demand less of the good, all other factors held constant.

Prices of Related Goods

• Goods are substitutes if one good can be used in the place of the other.
• When a fall in the price of one good reduces the demand for another good, the two goods are called substitutes.
• Goods are said to be complements if they are used in conjunction with each other.
• When a fall in the price of one good increases the demand for another good, the two goods are called complements

Taste Patterns on Consumers

• T takes on larger values as consumers perceive a good becoming higher in quality, more fashionable, more healthful, or more desirable in any way.
• A decrease in T corresponds to a change in consumer tastes away from a good or service as consumers perceive falling quality, or displeasing appearance, or diminished healthfulness.

Expectations

• Expectations of consumers also influence consumers' decisions to purchase goods and services.
• Consumers' expectations about the future price of a commodity can change their current purchasing decisions.

Number of Consumers

• An increase in the number of consumers in the market will increase the demand for a good.
• A decrease in the number of consumers will decrease the demand for a good, all other factors held constant.

Slope Parameter

• Q₁ = a + bP + cM + dPR + eT + fPE + gN where Qa, P, M, PR, T, PE, and N are as defined above, and a, b, c, d, e, f, and g are parameters.
• The intercept parameter a shows the value of Q when the variables P, M, PR, T, PE, and N are all simultaneously equal to zero.
• The other parameters, b, c, d, e, f, and g, are called slope parameters.
• They measure the effect on quantity demanded of changing one of the variables P, M, PR, T, PE, or N while holding the rest of these variables constant.
• The slope parameter b, for example, measures the change in quantity demanded per unit change in price; that is, b = ∆Q/∆P. As stressed earlier, Q₁ and P are inversely related, and b is negative because ∆Qa and ∆P have opposite algebraic signs.

Direct Demand Function

• A table, a graph, or an equation that shows how quantity demanded is related to product price, holding constant the five other variables that influence demand: Qd = f (P).
• Qd= f (P, M, PR) = f (P)

To Illustrate the Derivation

• Qd= 3,200 – 10P + 0.05M – 24PR
• Qd= 3,200 – 10P + 0.05(60,000) – 24(200) = 3,200 – 10P + 3,000 – 4,800 = 1,400 – 10P If P = $60 -> Qd= 1,400 – (10 x 60) = 800 If P = $40 -> Qd= 1,400 – (10 x 40) = 1,000

Demand Schedule

• A demand schedule (or table) shows a list of several prices, and the quantity demanded per period of time at each of the prices.

Demand Curve

• A graph showing the relation between quantity demanded and price when all other variables influencing quantity demanded are held constant.

Inverse Demand Function

• The demand function when price is expressed as a function of quantity demanded: P= f(Qd).
• Every point on a demand curve can be interpreted in either of two ways: the maximum amount of a good that will be purchased if a given price is charged or the maximum price that consumers will pay for a specific amount of a good.
• Demand price - The maximum price consumers will pay for a specific amount of a good or service.

Movements along Demand

• A Change in Quantity Demand is a movement along a given demand curve that occurs when the price of the good changes, all else constant.
• A Shift in demand occurs when any one of the five variables held constant when deriving a direct demand function from the general demand relation changes value.
• A new demand function results, causing the entire demand curve to shift to a new location.

Implementation

• An Increase in Demand is a change in the demand function that causes an increase in quantity demanded at every price and is reflected by a rightward shift in the demand curve.
• A Decrease in Demand is a change in the demand function that causes a decrease in quantity demanded at every price and is reflected by a leftward shift in t.
• Determinants of Demand: Variables that change the quantity demanded at each price and that determine where the demand curve is located: M, PR, 7, PE, and N.
• A Change in Demand is a shift in demand, either leftward or rightward, that occurs only when one of the five determinants of demand changes.