91Ó°ÊÓ

Demand and supply functions are fundamental concepts in economics. They describe the relationship between the quantity of a good consumers want to buy and what suppliers want to sell. The demand function, given by \( Q = a - bp \), shows a negative correlation between price \( p \) and quantity \( Q \). This means as the price increases, the quantity demanded generally decreases, illustrating the law of demand.
Meanwhile, the supply function \( Q = c + ep + ft \) depicts a positive relationship between price and quantity supplied. As price rises, so does the quantity that producers are willing to supply, illustrating the law of supply.
Interestingly, the supply function includes a term \( ft \), indicating that supply can also be influenced by external factors like temperature.
This addition allows us to explore how shifts in these external factors can influence the equilibrium outcomes in a market over time.

In a market, equilibrium is achieved where the demand equals the supply. This is the point where both consumers' and producers' interests are perfectly matched, leading to a stable market condition.
To find the equilibrium price \( p \), we set the demand function equal to the supply function: \[ a - bp = c + ep + ft \]
Solving for \( p \) gives us: \[ p = \frac{a - c - ft}{b + e} \]. This formula tells us that equilibrium price is affected by demand, supply factors, and external conditions like temperature \( t \) which is part of the supply equation.
Plugging \( p \) back into the demand function helps us find the equilibrium quantity \( Q \): \[ Q = a - b\left(\frac{a - c - ft}{b + e}\right) \] which can be simplified further.
In essence, equilibrium in the market ensures the quantity demanded by consumers matches the quantity suppliers are willing to provide.

Temperature can have significant impacts on market equilibrium. In the given supply function, \( Q = c + ep + ft \), the term \( ft \) indicates temperature's role.
As temperature \( t \) increases, it directly influences the supply equation by adding to the overall supply. This implies that higher temperatures can lead to increased supply, holding everything else constant.
However, the increased temperature negatively affects the equilibrium price \( p \): \[ p = \frac{a - c - ft}{b + e} \]. As temperature rises, the \( -ft/(b+e) \) component becomes larger negative value, thus reducing \( p \).
Thus, we see a drop in price due to additional supply influenced by higher temperature.
This scenario is a clear example of how natural factors, like temperature, can dynamically affect economic equilibrium by altering both supply and price.