Minggu 6 Aplikasi Fungsi Non Linier Pada Bisnis (1)

Summary

In this educational video, Nora Amelda from Telkom University's Business Management program explains the application of nonlinear functions in business, particularly in market demand, supply, and equilibrium. She discusses how quadratic functions can represent these concepts and walks through an example of calculating market equilibrium without taxes. The impact of taxes on supply and demand curves is also explored, showing how price and quantity equilibrium shift. The video further details the process of calculating the new equilibrium when taxes are imposed, providing a comprehensive understanding of nonlinear economic functions.

Takeaways

• 😀 Nonlinear functions in business applications, like demand, supply, market equilibrium, cost functions, and break-even points, share similarities with linear functions in analysis.
• 😀 Demand and supply curves in business can take nonlinear forms such as quadratic, circular segments, ellipse segments, hyperbola segments, or parabolic segments.
• 😀 Market equilibrium can be analyzed similarly for both linear and nonlinear functions, where the equilibrium occurs at the intersection of demand and supply curves.
• 😀 Nonlinear demand and supply functions can involve quadratic forms, and these can be analyzed by focusing on parts of the curve relevant to equilibrium.
• 😀 Changes in market conditions like taxes or subsidies alter the equilibrium by affecting the supply curve, causing shifts in both price and quantity.
• 😀 Taxes raise the equilibrium price and lower the equilibrium quantity, as suppliers increase the price to accommodate the tax burden.
• 😀 The example problem demonstrates how to find market equilibrium for a given nonlinear demand and supply function by setting the quantity demanded equal to the quantity supplied.
• 😀 In the example, the equilibrium price (Pe) and equilibrium quantity (Qe) were calculated using quadratic equations, with Pe = 3 and Qe = 10.
• 😀 Introducing a specific tax per unit alters the supply function, requiring the adjustment of the equilibrium calculation to account for the tax.
• 😀 After a tax is introduced, the new equilibrium price and quantity are calculated using the modified supply function, which results in a new equilibrium price of 3.63 and quantity of 5.82.
• 😀 The script also covers how to calculate the tax burden on consumers and producers, by determining the price differences before and after tax and then multiplying by the new equilibrium quantity.

Q & A

What is the primary focus of the script?

The primary focus of the script is explaining the application of nonlinear functions in business scenarios, such as demand, supply, market equilibrium, cost functions, and the effect of taxes and subsidies on these economic models.

What are the key differences between linear and nonlinear demand and supply functions?

Linear demand and supply functions are straight lines, whereas nonlinear demand and supply functions can take various forms, such as quadratic, circular, elliptical, hyperbolic, or parabolic shapes. Nonlinear functions provide more flexibility in modeling real-world market behavior.

How is market equilibrium analyzed when dealing with nonlinear demand and supply functions?

Market equilibrium for nonlinear demand and supply functions is analyzed similarly to linear functions. It occurs where the quantity demanded (QD) equals the quantity supplied (QS). This equilibrium is determined by the intersection of the demand and supply curves, even if the curves are nonlinear.

What happens to market equilibrium when taxes or subsidies are introduced?

Taxes and subsidies shift the supply curve. In the case of taxes, the price at which producers are willing to sell increases, and the equilibrium quantity decreases. For subsidies, the price offered by producers decreases, affecting the equilibrium price and quantity.

How is the effect of taxes on market equilibrium modeled in the example?

In the example, a specific tax per unit is introduced, which shifts the supply curve upward by the amount of the tax. The new equilibrium is found by solving the adjusted supply equation, considering the impact of the tax on the price and quantity.

What is the formula used for finding the new market equilibrium after the imposition of a tax?

The new supply function after the imposition of a tax is represented as the original supply function plus the tax amount. This adjusted function is then substituted into the demand function to find the new equilibrium price and quantity.

How do you calculate the price and quantity equilibrium after a tax is imposed?

After the tax is imposed, you substitute the adjusted supply function (which includes the tax) into the demand function and solve for the equilibrium price and quantity. The equilibrium price is then found by solving the quadratic equation that results from this substitution.

What does the script explain about calculating tax burdens on consumers and producers?

The script explains how to calculate the tax burden on consumers and producers by comparing the equilibrium prices before and after the tax. The consumer burden is the difference in price paid by consumers before and after the tax, while the producer burden is the difference in the price producers receive.

How is the total tax paid to the government calculated?

The total tax paid to the government is calculated by multiplying the tax per unit by the new equilibrium quantity after the tax is imposed.

What is the significance of the quadratic equations used in the examples?

The quadratic equations used in the examples are important for determining the new equilibrium prices and quantities in cases where the supply and demand functions are nonlinear. These equations help find the precise solution by factoring or using the quadratic formula.