Question

Explain how to derive a total expenditures (TE) curve.

Short answer

The Total Expenditures curve is derived by first understanding the fundamental concepts of total expenditure and price elasticity. You then categorize the price elasticity into elastic, inelastic, and unit elastic. The next step is plotting the curve using the unit price and quantity values. The total expenditure calculation is obtained by multiplying the price per unit by the quantity demanded. The shape the curve takes depends on whether demand is categorized as elastic, inelastic or unit elastic

Step-by-step solution

Understanding Basic Concepts

The first step is understanding what the Total Expenditure is. Total Expenditure (TE) represents the overall amount of money that consumers spend on a good. It is calculated as the product of the price (P) per unit of the good and the quantity demanded (Q), i.e., \( TE = P \times Q \). Additionally, understand the concept of price elasticity of demand, which measures the responsiveness of the quantity demanded of a good or service to a change in its price.

Classifying Price Elasticity

The price elasticity of demand can be broken down into three categories: elastic, inelastic, and unit elastic. When demand is elastic (\( E > 1 \)), a decrease in price increases total expenditure and vice versa. When demand is inelastic (\( E < 1 \)), a decrease in price decreases total expenditure and vice versa. Finally, when the demand is unit elastic (\( E = 1 \)), total expenditure remains constant regardless of the price.

Plotting the Total Expenditure Curve

After understanding these basic concepts, the TE curve can be plotted. On the y-axis we have Total Expenditure and on the x-axis we have Quantity. Start by plotting points for varying values of quantity and their corresponding total expenditure (calculated as stated in Step 1). After plotting these points, connect them to get the TE curve. The shape of this curve will depend on whether demand is elastic, inelastic, or unit elastic. In elastic range, the curve slopes upward, in inelastic range it slopes downward and it's flat in the unit elastic range.

Key concepts

Price Elasticity of Demand

Price elasticity of demand is a key concept in understanding how consumers react to changes in price. This elasticity measures how much the quantity demanded of a good responds to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. This can be expressed mathematically as:\[E_d = \frac{\% \Delta Q}{\% \Delta P}\]Depending on the value of the elasticity, demand can be categorized as:

• Elastic: Demand is elastic if the elasticity is greater than 1. This means consumers are very responsive to price changes. For example, if a 10% decrease in price leads to a 20% increase in quantity demanded, the demand is elastic.
• Inelastic: Demand is inelastic if the elasticity is less than 1, indicating that consumers are not very responsive to price changes. For example, a 10% decrease in price might only lead to a 5% increase in quantity demanded.
• Unit Elastic: Demand is unit elastic when the elasticity exactly equals 1. This means the percentage change in quantity demanded is exactly the same as the percentage change in price.

Understanding the elasticity of demand helps businesses decide how changing prices might impact total revenue, reflecting its crucial role in the total expenditure curve.

Quantity Demanded

The quantity demanded refers to the total amount of a product that consumers are willing and able to purchase at a given price during a specific time period. It is one of the core components in calculating total expenditure and plays a vital role in economic analysis. When evaluating the market, it is important to recognize how quantity demanded shifts according to price changes. This relationship is what creates the demand curve, typically downward sloping, indicating that as price decreases, quantity demanded tends to increase, and vice versa. A few factors influencing quantity demanded include:

• Price of the Good: Directly affects the amount consumers are willing to buy. As prices drop, the quantity demanded usually rises.
• Income Levels: Higher income often increases consumers' ability to buy more, affecting quantity demanded positively.
• Tastes and Preferences: Changes in consumer preferences can shift the quantity demanded even if the price remains constant.

These dynamics of quantity demanded are crucial for understanding the TE curve, as they determine how much consumers spend at different price levels.

Price Per Unit

The price per unit is the cost for each individual good or service. This component is crucial in calculating both total expenditure and understanding the dynamics of supply and demand.Total Expenditure (TE) is calculated using the formula:\[TE = P \times Q\]where \(P\) represents the price per unit, and \(Q\) represents the quantity demanded. Fluctuations in the price per unit can significantly affect consumer spending and consequently, the total expenditure. Some key points to consider about price per unit include:

• Direct Impact on Spending: Lowering the price can enhance affordability, possibly boosting quantity demanded and impacting the TE curve.
• Market Competition: Competitors’ pricing can influence a business's price per unit decisions to remain competitive.
• Perceived Value: Consumers may associate price with quality, affecting purchasing decisions beyond mere cost considerations.

Understanding the pivotal role of price per unit helps paint a complete picture of market behavior, as it directly affects both consumer expenditure and firm revenue.