Question

Suppose that the market demand for 32-oz. wide mouth Nalgene bottles is Q = 50,000p^-1.076, where Q is the quantity of bottles per week and p is the price per bottle. The market supply is Q = 0.01p^7.208. What is the equilibrium price and quantity? What is the consumer surplus? What is the producer surplus?

Answer 1

To find the equilibrium price and quantity for Nalgene bottles, set the demand and supply functions equal and solve for the price, then plug that into either function. Consumer surplus is the difference between what consumers are willing to pay versus what they pay, while producer surplus is what producers get over their minimum acceptable price.

Step-by-step explanation:

To find the equilibrium price and quantity for 32-oz. wide mouth Nalgene bottles, we need to set the market demand function Q = 50,000p^-1.076 equal to the market supply function Q = 0.01p^7.208 and solve for p. Once we find the equilibrium price, we substitute it back into either the demand or supply function to find the equilibrium quantity.

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay, and producer surplus is the difference between the price at which producers are willing to sell and the price they actually receive.

To calculate consumer and producer surplus, we would need to determine the area above the supply curve and below the demand curve up to the equilibrium price. This involves integrating the demand function from zero to the equilibrium price for consumer surplus and integrating the supply function from zero to the equilibrium price for producer surplus.

Answer 2

Equilibrium price and quantity

$6.44 and 6768

Consumer surplus

$571,081

Producer Surplus

$5,288

Step-by-step explanation:

In this question, we are asked to calculate equilibrium price and quantity, consumer surplus and producer surplus.

Please check attachment for complete solution and step by step explanation