Market equilibrium with a power of 3 function

Previous knowledge of the market equilibrium calculation

• You need a demand and a supply function to calculate the market equilibrium with a power 3 function in math.
• Note that the demand function reflects the behavior of the customer, the supply curve of the supplier for a product on the market.
• You decide with the Functions the equilibrium quantity, the equilibrium price, can also determine the consumer and producer surplus.
• The consumer surplus is the amount of money that consumers would be willing to pay in an emergency, while the producer surplus is the price at which the provider is still willing to buy the product to manufacture.
• In your calculations you will find the market equilibrium where the price of the goods offered corresponds exactly to the price of the products in demand.
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Calculate equilibrium using a power-3 function in math

• To compute the market equilibrium within the math class, you need the supply and demand functions, both of which are not power-3 functions, and set them equal. Using the example of P_A.(x) = 2x + 2 and P_N(x) = 1/2 _* (36 - x²) applies 2x + 2 = 1/2 _* (36 - x²).
• After you've calculated the bracket, set the equation to 0: -1/2 x² - 2x + 16 = 0 and multiply by -1/2.
• After multiplying you get x² + 4x -32 = 0 and use the p-q formula to calculate the values ​​for x₁ and x₂ the end. The result is x₁ = 4 and x₂ = - 8. Since there are no negative units of measure (ME), the equilibrium amount is 4 ME.
• If you now insert the equilibrium quantity x = 4 into the supply function, you get the equilibrium price P._A.(4) = 2 _* 4 + 2 = 10 monetary units (MU).
• The consumer surplus and the producer surplus are calculated with a power of 3, since you have to find the antiderivative of the supply and demand function.