You need to have read the discussion on supply and demand...

You need to have read the discussion on supply and demand preceding Example $6,$ as well as Example 6 itself. In each exercise, assume that the price $p$ is in dollars. Assume that the supply and demand functions for a commodity are as follows. Supply: $q=200 p ;$ Demand: $q=9600-400 p ;$ for $p \geq 0$ (a) If the price is set at $$ 6,$ will there be a shortage or a surplus of the commodity? What if the price is doubled? (b) If the price is $$ 20,$ will there be a shortage or a surplus? (c) Find the equilibrium price and the corresponding equilibrium quantity.

You need to have read the discussion on supply and demand preceding Example $6,$ as well as Example 6 itself. In each exercise, assume that the price $p$ is in dollars.
Assume that the supply and demand functions for a commodity are as follows. Supply: $q=200 p ;$ Demand: $q=9600-400 p ;$ for $p \geq 0$
(a) If the price is set at $$ 6,$ will there be a shortage or a surplus of the commodity? What if the price is doubled?
(b) If the price is $$ 20,$ will there be a shortage or a surplus?
(c) Find the equilibrium price and the corresponding equilibrium quantity.

Key Concepts

Market Equilibrium

Market equilibrium is the point where the quantity supplied equals the quantity demanded. At this equilibrium, there is no inherent market pressure to change the price, as supply perfectly meets demand. This concept is central to understanding how prices adjust in a free market to balance the interests of both buyers and sellers.

Shortage and Surplus

A shortage occurs when the quantity demanded exceeds the quantity supplied at a given price, indicating that consumers are willing to buy more than what is available, often leading to upward pressure on prices. Conversely, a surplus occurs when the quantity supplied exceeds the quantity demanded, meaning that there is more of the commodity available than consumers want to purchase at that price, typically resulting in downward pressure on prices.

Demand Function

A demand function describes how the quantity demanded of a commodity varies with its price, usually indicating that as the price decreases, consumers are willing to buy more. This inverse relationship reflects the basic economic principle that lower prices make goods more affordable and attractive to consumers.

Supply Function

A supply function represents the relationship between the price of a commodity and the quantity of that commodity that producers are willing to produce and sell. It typically suggests that as prices increase, the quantity supplied also increases, reflecting the incentive for producers to supply more at higher profit margins.

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