Question

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?

Short answer

The equations for supply and demand are Qs = 2/3P and Qd = 38 - 2P respectively. At a price of \$9, price elasticity of demand is -0.9 and of supply is 1. At \$12, price elasticity of demand is -1.71 and of supply is 1. In a free market, the U.S. price will be \$9 and fiber imports will be 14 million lbs.

Step-by-step solution

Identifying Supply and Demand Equations

Firstly, let's find the slope of the supply and demand function using the formula: slope = (y2 - y1) / (x2 - x1), taking the simplest pair. For supply, let's choose the points (3,2) and (6,4), thus the supply slope would be (4-2)/(6-3) = 2/3. Now to find the y-intercept, substitute one point and the slope into the formula y = mx + c, thus giving the supply equation as Qs = (2/3)P. Similarly, for demand, let's choose the points (3,34) and (6,28), giving the demand slope as (28-34)/(6-3) = -2. Substituting, the demand equation becomes Qd = 38 - 2P.

Determine Price Elasticity of Demand and Supply

The price elasticity of demand is given by the formula: E = (dQ/dP)*(P/Q). For P = \$9, from the demand equation, Q = 38 - 2(9) = 20, substituting gives Ed = -2 * (9/20) = -0.9. Similarly, for P = \$12, Q = 38 - 2(12) = 14, giving Ed = - 2 * (12/14) = -1.71. The price elasticity of supply is calculated in the same manner. At P = \$9, Q = (2/3) * 9 = 6, giving Es = (2/3) * (9/6) = 1. At P = \$12, Q = (2/3) * 12 = 8, so Es = (2/3) * (12/8 ) = 1.

Identify U.S. Price and Level of Fiber Imports

In a free market, the U.S. price will be the world price, \$9. The quantity demanded at this price is Qd = 38 - 2 * 9 = 20 million lbs, and domestically supplied quantity is Qs = (2/3) * 9 = 6 million lbs. So, the level of fiber imports = Qd - Qs = 20 - 6 = 14 million lbs.

Key concepts

Supply and Demand Equations

In economics, supply and demand equations describe how the market decides the amount of a good or service to produce and consume based on price. Let's break it down for the U.S. market of vegetable fiber.

For supply, the equation is found using selected price and supply data points, calculated as \( Q_s = \frac{2}{3}P \). This tells us that as the price (\( P \)) increases, the quantity supplied \( Q_s \) also increases, demonstrating a direct relationship.

Demand works a bit differently. Using selected data, the demand equation is \( Q_d = 38 - 2P \). Here, the negative sign in front of \( 2P \) shows an inverse relationship: as the price goes up, the quantity demanded \( Q_d \) decreases.

Understanding these equations helps us predict how changes in price affect supply and demand in the U.S. market for vegetable fiber.

Competitive Market

A competitive market is one where numerous buyers and sellers interact, so no single entity can control the market price. In such a market, the price is determined by the equilibrium of supply and demand.

For vegetable fiber traded globally, the competitive market ensures that the world price is maintained at \( \\(9 \) per pound. This means that at \( \\)9 \), the price is externally fixed and U.S. suppliers and consumers must adapt to it rather than setting it themselves.

• U.S. suppliers will determine how much to produce based on this set price.
• Consumers will decide their consumption levels depending on their needs and price sensitivity at this fixed price.

In essence, competitive markets like this lead to efficient distribution of goods, reflecting both global supply conditions and domestic demand preferences.

Fiber Imports

Fiber imports are crucial in balancing domestic demand and supply in the U.S. At the world price of \( \$9 \), we see an interesting dynamic.

The quantity demanded domestically at this price is 20 million pounds, but only 6 million pounds are supplied by U.S. producers. This gap is filled by importing the difference, which totals 14 million pounds.

• This means U.S. consumers rely heavily on imports to meet their needs.
• Such a reliance ensures that domestic shortages don't occur, keeping the market stable.

Ultimately, importing allows the U.S. to access unlimited quantities at the world price, ensuring that domestic demands are met without pushing domestic prices higher.