Question

If four firms in a competitive industry have supply schedules given by the following equations: $$ \begin{array}{ll} \mathrm{Q}_{1}{ }^{\mathrm{S}}=16+4 \mathrm{P} & \mathrm{Q}_{3}{ }^{\mathrm{S}}=32+8 \mathrm{P} \\ \mathrm{Q}_{2}{ }^{\mathrm{S}}=5-5 \mathrm{P} & \mathrm{Q}_{4}{ }^{\mathrm{S}}=60-10 \mathrm{P} \end{array} $$ What is their combined supply?

Short answer

The combined supply of the four firms in the competitive industry is given by the equation \(Q_T^S = 113 - 3P\).

Step-by-step solution

Write down the individual supply schedules

Using the information provided in the exercise, the supply schedules for the four firms are as follows: \[ Q_1^S = 16 + 4P \] \[ Q_2^S = 5 - 5P \] \[ Q_3^S = 32 + 8P \] \[ Q_4^S = 60 - 10P \]

Find the combined supply

Now, we will find the combined supply by adding up the supply schedules for all four firms: \[ Q_T^S = Q_1^S + Q_2^S + Q_3^S + Q_4^S \]

Substitute the individual supply schedules into the combined supply equation

Now, we substitute the individual supply schedules in the equation: \[ Q_T^S = (16 + 4P) + (5 - 5P) + (32 + 8P) + (60 - 10P) \]

Simplify the combined supply equation

Combine the similar terms in the equation: \[ Q_T^S = 16 + 4P + 5 - 5P + 32 + 8P + 60 - 10P \] \[ Q_T^S = (16 + 5 + 32 + 60) + (4P - 5P + 8P - 10P) \]

Calculate the combined supply

Now, simplify and calculate the combined supply: \[ Q_T^S = 113 - 3P \] The combined supply of the four firms in the competitive industry is given by: \[ Q_T^S = 113 - 3P \]

Key concepts

Supply Schedules

Understanding supply schedules is essential for any student studying economics. These schedules are essentially charts or equations expressing how much product a supplier is willing to provide at different price levels. The relationship is typically direct; as prices go up, suppliers are motivated to supply more, hoping to maximize profits.

For example, if a firm's supply schedule is represented as \( Q^S = a + bP \), where \( Q^S \) is the quantity supplied, \( P \) is the price, and \(a\) and \(b\) are constants, this equation tells us how much the firm will supply at any given price. If \(b\) is positive, there's a direct relationship — the firm will supply more as the price increases. However, if \(b\) is negative, the firm will supply less as the price increases, which may happen in cases of market anomalies or mismanagement.

For students, breaking down each term and understanding their significance is important. The constant \(a\) represents the base level of supply when the price is zero, and \(b\) shows how sensitive the supply is to price changes—known in economics as the price elasticity of supply.

Competitive Industry

A competitive industry is characterized by a large number of small firms, each of which has a relatively small market share and does not have the market power to influence prices. The products offered by the firms are also usually very similar, if not identical, which is why this type of market is sometimes referred to as a 'perfect competition'.

One key feature is that firms in a competitive industry are price takers. They must accept the market price as given and cannot charge more, as consumers would simply buy from a competitor offering a lower price. This market structure benefits consumers through lower prices and increased efficiency within the industry.

Firms operating in such industries can enter and exit the market relatively easily, which could lead to changes in total supply over time. Therefore, understanding the combined supply of a competitive industry can provide insights into market dynamics, such as how shifts in supply can affect product prices.

Market Supply

Market supply is the total quantity of a good or service that all producers in a market are willing and able to sell at different prices. It's a cornerstone concept in economics because it, combined with market demand, helps determine the equilibrium price and quantity for a good or service.

To calculate market supply, we sum up the individual supplies from all producers at each price level. As seen in the original exercise with the four firms, we add their supply schedules together to find the cumulative supply provided to the market at various prices. This process involves treating the market as an aggregation of all individual suppliers, each contributing their own quantity to the total supply.

For students, the combined supply calculation must be understood not just as an arithmetic sum but as the collective market behavior of producers responding to price signals. Factors like production costs, technology, and the number of sellers can shift the market supply, influencing prices and the overall economy.