A vegetable fiber is traded in a competitive world market,...

A vegetable fiber is traded in a competitive world market, and the world price is $\$ 9$ per pound. Unlimited quantities are available for import into the United States at this price. The U.S. domestic supply and demand for various price levels are shown as follows: $$\begin{array}{|c|c|c|} \hline \text { PRICE } & \begin{array}{c} \text { U.S. SUPPLY } \\ \text { (MILION LBS) } \end{array} & \begin{array}{c} \text { U.S. DEMAND } \\ \text { (MILIION LBS) } \end{array} \\ \hline 3 & 2 & 34 \\ \hline 6 & 4 & 28 \\ \hline 9 & 6 & 22 \\ \hline 12 & 8 & 16 \\ \hline 15 & 10 & 10 \\ \hline 18 & 12 & 4 \\ \hline \end{array}$$ a. What is the equation for demand? What is the equation for supply? b. At a price of $\$ 9,$ what is the price elasticity of demand? What is it at a price of $\$ 12 ?$ c. What is the price elasticity of supply at $\$ 9 ?$ At $\$ 12 ?$ d. In a free market, what will be the U.S. price and level of fiber imports?

A vegetable fiber is traded in a competitive world market, and the world price is $\$ 9$ per pound. Unlimited quantities are available for import into the United States at this price. The U.S. domestic supply and demand for various price levels are shown as follows:
$$\begin{array}{|c|c|c|}
\hline \text { PRICE } & \begin{array}{c}
\text { U.S. SUPPLY } \\
\text { (MILION LBS) }
\end{array} & \begin{array}{c}
\text { U.S. DEMAND } \\
\text { (MILIION LBS) }
\end{array} \\
\hline 3 & 2 & 34 \\
\hline 6 & 4 & 28 \\
\hline 9 & 6 & 22 \\
\hline 12 & 8 & 16 \\
\hline 15 & 10 & 10 \\
\hline 18 & 12 & 4 \\
\hline
\end{array}$$
a. What is the equation for demand? What is the equation for supply?
b. At a price of $\$ 9,$ what is the price elasticity of demand? What is it at a price of $\$ 12 ?$
c. What is the price elasticity of supply at $\$ 9 ?$ At $\$ 12 ?$
d. In a free market, what will be the U.S. price and level of fiber imports?

Key Concepts

Free Trade Equilibrium

In the context of international trade, the free market equilibrium is the price and quantity at which domestic supply and demand intersect when open to world trade. When a country allows imports at a fixed world price, it adjusts its domestic consumption and production accordingly, and the level of imports is determined as the gap between domestic demand and domestic supply at that price.

Price Elasticity of Demand

Price elasticity of demand measures how sensitive the quantity demanded is to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. This concept helps in understanding consumer behavior and is important when assessing how changes in market price affect overall market demand.

Price Elasticity of Supply

Similarly, the price elasticity of supply quantifies the responsiveness of the quantity supplied when the market price changes. It is computed as the percentage change in quantity supplied divided by the percentage change in price. This concept is vital for understanding producer behavior and analyzing how supply reacts to price fluctuations, which in turn affects market equilibrium.

Supply and Demand Analysis

This concept involves understanding how the quantity supplied by producers and the quantity demanded by consumers interact at various price levels. It is fundamental in determining market outcomes, such as equilibrium price and quantity, and is used to analyze the impacts of changes in market conditions like shifts due to policy or trade.

Deriving Linear Equations

When supply and demand data is provided in a tabular form, one common method is to derive the linear equations that represent the supply and demand curves. This process involves identifying two points from the data and using the slope-intercept form of a line to express the relationship between price and quantity, which is crucial for further analysis such as elasticity calculations and equilibrium determination.

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