Question

Suppose that 1,000 people in a market each have the same monthly demand curve for bottled water, given by the equation \(Q^{D}=100-25 P,\) where \(P\) is the price for a 12 -ounce bottle in dollars. a. How many bottles would be demanded in the entire market if the price is \(\$ 1 ?\) b. How many bottles would be demanded in the entire market if the price is \(\$ 2 ?\) c. Provide an equation for the market demand curve, showing how the market quantity demanded by all 1,000 consumers depends on the price.

Short answer

a. 75,000 bottles would be demanded in the entire market if the price is $1. b. 50,000 bottles would be demanded in the entire market if the price is $2. c. The market demand curve equation is \(Q^{D}_{market} = 1000 * (100-25 P)\).

Step-by-step solution

Determine the quantity demanded when the price is $1

To do this, substitute \(P = 1\) into the individual demand equation \(Q^{D}=100-25 P,\) which leads to \(Q^{D}=100-25*1 = 75\). This means each consumer would demand 75 bottles.

Multiply the individual demand by the total number of consumers

There are 1000 consumers in the market. By multiplying the per-consumer demand by the total number of consumers, we get the total market demand: \(1000 * 75 = 75,000\). So, 75,000 bottles would be demanded in the entire market when the price is $1.

Determine the quantity demanded when the price is $2

Do the same as in step 1 but this time, substitute \(P = 2\) into the equation \(Q^{D}=100-25 P,\) which results in \(Q^{D}=100-25*2 = 50\). Hence, each consumer demands 50 bottles at a price of $2 per bottle.

Multiply the individual demand by the total number of consumers for price $2

Analogous to step 2, multiply the per consumer demand by the total number of consumers to get market demand at price $2: \(1000 * 50 = 50,000\). Therefore, 50,000 bottles would be demanded in the entire market when the price is $2.

Provide an equation for the market demand curve

The market demand is calculated by multiplying the individual demand by the total number of consumers. Therefore, the market demand equation is \(Q^{D}_{market} = 1000 * (100-25 P)\). This equation shows how the market quantity demanded by all 1000 consumers depends on the price.

Key concepts

Market Demand

Market demand is the total quantity of a good or service that all consumers are willing and able to purchase at a given price level. It encompasses the individual demands of all potential buyers in a specific market. Understanding market demand is crucial because it helps businesses and policymakers gauge how changes in price affect overall consumption in a market.

When we calculated the market demand for bottled water in the exercise, we took into account the demand from each consumer and multiplied it by the number of consumers in the market. For instance, when the price of water was $1, each consumer wanted 75 bottles, leading to a total of 75,000 bottles for 1,000 consumers. This illustrates how individual demand translates into market demand.

The market demand curve can be graphed using these quantities at different price levels, typically showing a downward slope, meaning as the price decreases, demand increases. This is the fundamental law of demand in economics.

Price Elasticity

Price elasticity refers to the responsiveness of the quantity demanded of a good to a change in its price. When demand is elastic, a small change in price leads to a large change in the quantity demanded. Conversely, demand is inelastic when quantity demanded is relatively unresponsive to price changes.

In the exercise, when the price increased from \(1 to \)2, the quantity demanded by each consumer decreased from 75 to 50 bottles, showing that buyers were sensitive to price changes. This behavior can be quantified using the price elasticity of demand formula: \[Elasticity = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}\] An elasticity greater than 1 indicates elastic demand, less than 1 indicates inelastic demand, and exactly 1 shows unitary elasticity.

Understanding elasticity helps businesses set prices optimally to maximize revenue and helps economists understand consumer behavior in response to price shifts.

Microeconomic Analysis

Microeconomic analysis delves into the decision-making processes of individuals and firms. This aspect of economics focuses on supply, demand, and prices, examining how these elements interact in various market structures. It provides insights into how resources are allocated and how factors like price changes impact demand and supply.

In our bottled water example, microeconomic analysis helps explain how the individual demand curve of a consumer and the market demand curve are created. By analyzing step-by-step how individual demand is aggregated to form market demand, we see the microeconomic principles in action.

• Microeconomics examines topics like consumer behavior, which affects and is affected by the availability and prices of goods.
• It looks at market equilibrium, where supply equals demand, and explores how shifts in these curves affect prices and quantities.

Microeconomic analysis is fundamental for understanding the broader picture of how economies function, focusing on details of smaller units such as individuals and firms.