Question

Refer to Example 2.10 (page 83 ), which analyzes the effects of price controls on natural gas. a. Using the data in the example, show that the following supply and demand curves describe the market for natural gas in \(2005-2007\): $$\begin{array}{ll} \text { Supply: } & Q=15.90+0.72 P_{G}+0.05 P_{O} \\ \text { Demand: } & Q=0.02-1.8 P_{G}+0.69 P_{O} \end{array}$$ Also, verify that if the price of oil is \(\$ 50\), these curves imply a free- market price of \(\$ 6.40\) for natural gas. b. Suppose the regulated price of gas were \(\$ 4.50\) per thousand cubic feet instead of \(\$ 3.00 .\) How much excess demand would there have been? c. Suppose that the market for natural gas remained unregulated. If the price of oil had increased from \(\$ 50\) to \(\$ 100,\) what would have happened to the freemarket price of natural gas?

Short answer

1. The equations correctly describe the supply and demand, and they do imply a free-market price of $6.40 for natural gas when price of oil is $50.\n2. The excess demand for gas can be calculated by subtracting the quantity supplied from the quantity demanded, when the regulated price of gas is $4.50.\n3. If the price of oil increases to $100, one can find the new free-market price of gas by equating the supply and demand equations and solving for the price of gas.

Step-by-step solution

Validate the Supply and Demand Equations

Substitute $P_O = 50$ into the supply and demand equations, then equate them to get the price of gas. The supply and demand are given by:\nSupply: \(Q_S=15.90 + 0.72 P_G + 0.05 P_O\)\nDemand: \(Q_D=0.02 - 1.8 P_G + 0.69 P_O\)\nFor equilibrium, \(Q_S = Q_D\), therefore we get:\n\(15.90 + 0.72 P_G + 0.05 * 50 = 0.02 - 1.8 P_G + 0.69 * 50\)\nSolving this for \(P_G\) should give us the free-market price of gas.

Compute Excess Demand for a Regulated Price

First calculate the quantity demanded and quantity supplied at $P_G = 4.50$. Then the excess demand is given by \(Q_D - Q_S\). Suppose the regulated price of gas is $P_G = 4.50$. We substitute these values in the demand and supply equations:\nFor supply: \(Q_S=15.90 + 0.72 * 4.50 + 0.05 * 50\)\nFor demand: \(Q_D=0.02 - 1.8 * 4.50 + 0.69 * 50\)\nThe excess demand is given by: \(Q_D – Q_S\)

Compute the New Free-Market Price of Gas

Repeat the process in Step 1, but this time with $P_O = 100$. This would give us the new free-market price of gas. If the price of oil increases to $100, then we have to solve the following equation for \(P_G\):\n\(15.90 + 0.72 P_G + 0.05 * 100 = 0.02 - 1.8 P_G + 0.69 * 100\)

Key concepts

Understanding Supply and Demand Equations

Supply and demand are the two fundamental concepts of economics that form the cornerstone of microeconomic theory. The equations for supply and demand show the relationship between the price of a good and the quantity of that good that suppliers are willing to produce or that consumers want to buy.

In mathematical terms, the supply equation typically has a positive relationship with price, which means as the price increases, the quantity supplied also increases. Conversely, the demand equation usually demonstrates a negative relationship with price, signifying that as the price increases, the quantity demanded decreases. The general form of these equations can be expressed as:

• Supply: \(Q_S = a + bP_G + cP_O\), where \(Q_S\) is the quantity supplied, \(P_G\) is the price of the good, \(P_O\) represents other factors that might affect supply, and \(a\), \(b\), and \(c\) are constants.
• Demand: \(Q_D = x + yP_G + zP_O\), with \(Q_D\) being the quantity demanded, and \(x\), \(y\), and \(z\) as constants.

These equations are used to find the point where the supply and demand curves intersect, which is known as the market equilibrium. This concept is crucial in understanding how markets function without external influences like government intervention.

Achieving Market Equilibrium

Market equilibrium occurs at the point where the quantity supplied equals the quantity demanded. This represents a state of balance in the market, where there's no tendency for the price to change, provided other factors remain constant. At equilibrium, the market-clearing price ensures that every consumer willing to pay the price can get the product and every supplier willing to sell at that price can find a buyer.

Mathematically, market equilibrium is found by setting the supply equation equal to the demand equation and solving for the price, signified as \(P_G\) in our case. This process is elegantly depicted in the textbook example where the supply and demand equations for natural gas are set equal to each other to find the free-market price.

Understanding market equilibrium helps in anticipating how market prices adjust in times of scarcity or surplus. In a perfectly competitive market, changes in supply or demand automatically lead to adjustments in price and quantity to reach a new equilibrium. However, when price controls are in place, this natural price mechanism is disrupted, leading to different market outcomes.

Effects of Price Regulation

Price controls are regulatory measures governments use to manipulate the natural functioning of the supply and demand in the marketplace. There are two primary forms of price controls: price ceilings (maximum prices) and price floors (minimum prices).

When a price ceiling, like a regulated price on natural gas, is set below the market-clearing price, it leads to excess demand or a shortage. This is because at the lower price, more consumers want to buy the gas than what is being supplied, leading to scarcity.

Similarly, a price floor set above the market equilibrium creates a surplus, with suppliers producing more than consumers are willing to buy at the increased price. The controlled price of \($4.50\) for natural gas, as mentioned in the textbook, would result in a specific excess demand quantity, calculated by finding the difference between the quantity demanded and quantity supplied at that price.

Price regulation can lead to inefficiencies in the market, such as underproduction, overproduction, or the misallocation of resources. It is essential for students studying microeconomics to understand the implications of price controls, as they represent significant deviations from the equilibrium outcomes predicted by unfettered market forces.