As background you need to have read the discussion on supply...

As background 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.

As background 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.

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Key Concepts

Surplus and Shortage

A surplus occurs when the quantity supplied exceeds the quantity demanded at a given price, leading to excess supply. Conversely, a shortage happens when the quantity demanded surpasses the quantity supplied, resulting in a deficit. These conditions are key indicators of market imbalances that drive price corrections.

Supply and Demand

Supply and demand are fundamental economic principles that describe the relationship between the quantity of a commodity that producers are willing to sell at various prices and the quantity that consumers are willing to buy. The supply function usually indicates a direct relationship with price, while the demand function shows an inverse relationship.

Market Equilibrium

Market equilibrium is reached when the quantity supplied equals the quantity demanded, resulting in a stable market price where there is neither excess supply nor shortage. This balance is crucial for understanding how prices adjust naturally in competitive markets.

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