ESPA4122 Matematika Ekonomi - Penerapan Fungsi Linear

Summary

This educational video from Universitas Terbuka covers the application of linear functions in economics, focusing on demand and supply functions, market equilibrium, and the impact of taxes and subsidies. Key topics include calculating equilibrium prices and quantities using linear equations, as well as the effects of taxes (both specific and proportional) and subsidies on the market. The session also explores how to handle multiple goods in market equilibrium calculations. The lecture provides valuable insights for students, helping them grasp essential concepts for analyzing economic models and real-world market behaviors.

Takeaways

• 😀 Linear functions are commonly used to model various economic problems such as demand, supply, and market equilibrium.
• 😀 The demand function is typically represented as Q = a - bP or P = a - bQ, where Q is quantity and P is price.
• 😀 The supply function is often written as Q = -a + bP or P = a + bQ, representing the relationship between price and quantity supplied.
• 😀 Market equilibrium occurs when the quantity demanded equals the quantity supplied (Qd = Qs), which determines the market price and quantity.
• 😀 To find market equilibrium, set the demand function equal to the supply function and solve for both price and quantity.
• 😀 Example: For the demand function P = 15 - Q and the supply function P = 3 + 0.5Q, the equilibrium price (P) is 7 and the equilibrium quantity (Q) is 8.
• 😀 Taxes shift the supply curve, causing a higher price and lower quantity at the new market equilibrium.
• 😀 Example: With a tax of 3 per unit, the new equilibrium price becomes 9 and the equilibrium quantity decreases to 6.
• 😀 Subsidies lower the price of goods by shifting the supply curve downwards, leading to a higher quantity and a lower price at equilibrium.
• 😀 Example: A subsidy of 1.5 per unit leads to a new equilibrium with price reduced to 6 and quantity increased to 9.
• 😀 Proportional taxes (like a percentage of the price) also affect both demand and supply curves, leading to changes in equilibrium price and quantity.
• 😀 When analyzing multiple goods, the equilibrium for each good must be determined by solving the interdependent system of equations for both goods.

Q & A

What is the purpose of using linear functions in economics?

Linear functions are used in economics to model various economic scenarios, such as demand, supply, market equilibrium, cost, revenue, profit, and budget constraints. They provide a simplified, straight-line representation of relationships between variables.

What is the demand function and how is it expressed?

The demand function shows the relationship between the quantity demanded (Q) and the price (P) of a good. It is commonly expressed as Q = a - bP, where 'a' is a constant, 'b' is the coefficient, and 'P' is the price. This function is typically downward sloping, indicating that as price decreases, quantity demanded increases.

How does the supply function differ from the demand function?

The supply function, represented as Q = -a + bP or P = a + bQ, describes the relationship between the quantity supplied (Q) and the price (P). Unlike the demand function, the supply function is upward sloping, meaning that as price increases, quantity supplied increases.

What is market equilibrium, and how is it determined?

Market equilibrium occurs when the quantity demanded (Qd) equals the quantity supplied (Qs). It is determined by finding the point where the demand and supply curves intersect. At this point, both the price and quantity are stable.

How is the equilibrium price and quantity calculated in an example problem?

In the example, the demand function is P = 15 - Q and the supply function is P = 3 + 0.5Q. Setting the demand equal to the supply (Qd = Qs), we solve the equations to find that the equilibrium quantity is 8, and the equilibrium price is 7.

What happens to market equilibrium when a tax is introduced?

When a tax is introduced, it shifts the supply curve upward by the amount of the tax. This results in a higher equilibrium price and a lower equilibrium quantity, as the tax increases the cost of supplying the good.

How does a specific tax affect the equilibrium price and quantity in the market?

In the case of a specific tax, such as 3 per unit, the supply function shifts upward by the amount of the tax. This causes the new equilibrium to occur at a higher price and a lower quantity. For example, the new equilibrium price might be 9, and the equilibrium quantity might be 6.

What is the difference between specific and proportional taxes in terms of their effects on the market?

A specific tax is a fixed amount per unit of good, whereas a proportional tax is based on a percentage of the price. A specific tax shifts the supply curve upward by a constant amount, while a proportional tax changes the price dynamically based on the price level.

How does a subsidy affect the market equilibrium?

A subsidy lowers the effective price for consumers by reducing the cost for producers. This shifts the supply curve downward, resulting in a lower equilibrium price and a higher equilibrium quantity, as the market price decreases and more goods are supplied.

How is equilibrium affected when there is a subsidy in place, and what is an example?

With a subsidy, the price for consumers is lower, and the quantity supplied increases. For example, if the government offers a subsidy of 1.5 per unit, the new equilibrium may occur at a price of 6, and the equilibrium quantity could rise to 9.