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In both the United States and France, the demand for haircuts is given by \(Q^{D}=300-10 P\) But in the United States, the supply is given by \(Q^{S}=-300+20 P\), while in France, the supply is given by \(Q^{S}=-33.33+6.67 P\) a. Graph supply and demand for haircuts for each country. (Use the same scale on each axis and graph carefully!) b. Solve for the equilibrium price and quantity of a haircut in each country. c. Suppose that the demand for haircuts in the United States increases by 100 units at each price, so the new demand is \(Q^{D}=400-10 P\) Place this new demand curve in the appropriate graph, and solve for the new equilibrium price and quantity in the United States. d. Suppose that, in a similar fashion, the demand for haircuts in France increases by 100 units at each price. Add the new demand curve for haircuts to the appropriate graph, and solve for the new equilibrium price and quantity. e. Drawing on your answers to (c) and (d), comment on the following statement: "The impact of an increase in demand depends critically on the slope of the supply curve."

Step by step solution

01

Write Down Equations

For each country, identify the demand and supply equations. In the United States, demand is given by \( Q^{D}_{US} = 300 - 10P \) and supply is \( Q^{S}_{US} = -300 + 20P \). In France, demand is \( Q^{D}_{FR} = 300 - 10P \) and supply is \( Q^{S}_{FR} = -33.33 + 6.67P \).

02

Graph Initial Supply and Demand Curves

Plot the demand and supply curves for both the United States and France using the equations identified. For the US, the demand curve is a downward slope originating at \( P = 30, Q^{D} = 0 \) and ends at \( P=0, Q^{D}=300 \). The supply curve starts at \( P=15, Q^{S}=0 \) and increases with a slope of 20 for the US. Similarly, plot the graphs for France using the given equations and scales.

03

Determine Equilibrium Price and Quantity

Set the supply equal to the demand for both countries to find the equilibrium. For the US: \( 300 - 10P = -300 + 20P \). Solving gives \( P = 20 \) and \( Q = 100 \). For France: \( 300 - 10P = -33.33 + 6.67P \), solving gives \( P \approx 20 \), which leads to \( Q \approx 100 \).

04

Adjust Demand in the US and Solve for New Equilibrium

Increase US demand by 100 units and use the new equation \( Q^{D} = 400 - 10P \). Solve \( 400 - 10P = -300 + 20P \) to find the new equilibrium: \( P=23.33 \), \( Q=166.67 \).

05

Adjust Demand in France and Solve for New Equilibrium

Similarly, raise France's demand by 100 units: \( Q^{D} = 400 - 10P \). Solve \( 400 - 10P = -33.33 + 6.67P \) to get \( P \approx 24.44 \), \( Q \approx 155.56 \).

06

Analysis of Demand Increase Impact

The increase in demand causes a larger price change in the United States due to its steeper supply curve compared to France. The equation for supply in the United States has a steeper slope (20) compared to France (6.67), indicating a larger response to demand changes in terms of price.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Supply and Demand Analysis

Supply and demand analysis is fundamental in microeconomics for determining how prices and quantities are set in markets. In any market, the demand curve represents consumer preferences, while the supply curve reflects producers' willingness to sell goods or services. The intersection point of these curves indicates the equilibrium price and quantity.

For example, in the United States and France, the demand for haircuts was initially expressed by the same equation: \(Q^D = 300 - 10P\). This equation shows an inverse relationship between price \(P\) and quantity demanded \(Q^D\); as prices increase, the demand decreases.

Supply curves, on the other hand, typically have a positive slope, implying a direct relationship between price and the quantity supplied \(Q^S\). In this context, the US supply equation \(Q^S = -300 + 20P\) describes how supply increases as price rises. Similarly, in France, the supply equation \(Q^S = -33.33 + 6.67P\) tells us the same, though with a gentler slope.

• This foundational analysis allows economists to predict shifts in market equilibrium.
• Understanding supply and demand helps analyze the effects of policy changes, taxes, or technological advancements.

Equilibrium Price and Quantity

In a competitive market, equilibrium is achieved when supply equals demand. At this point, the market is in balance, resulting in an agreed-upon price and quantity where neither excess supply nor excess demand exists.

To find the equilibrium, set the demand and supply equations equal to each other. In our example, with original data for both countries, we use the US: \(300 - 10P = -300 + 20P\). Solving this equation yields \(P = 20\) and \(Q = 100\).

In France, setting \(300 - 10P\) equal to \(-33.33 + 6.67P\) results in \(P \approx 20\) and \(Q \approx 100\) as well. Thus, initially, both countries shared similar equilibrium states, although influenced by different curve slopes.

• An equilibrium efficiently allocates resources without wasting them.
• Mismatch between supply and demand pushes the market towards back equilibrium.

Impact of Demand Changes

When demand patterns change, it shifts the entire demand curve, leading to a new equilibrium price and quantity. For instance, if there is an increased desire for a product or service, demand rises, shifting the curve to the right.

In the US, where demand increased by 100 units, the new equation is \(Q^D = 400 - 10P\). Solving it alongside the supply equation \(-300 + 20P\), we find that the new price \(P\) rises to approximately \(23.33\), and quantity \(Q\) increases to \(166.67\).

Similarly, in France, using \(400 - 10P\) against \(-33.33 + 6.67P\), the equilibrium shifts to \(P \approx 24.44\) and \(Q \approx 155.56\).

• This shift represents the market's natural adjustment to increased demand.
• Sellers respond to the increased willingness of consumers to pay by supplying more at higher prices.

Slope of Supply Curve

The slope of the supply curve is crucial in determining how sensitive the price equilibrium is to changes in market demand. A steeper slope indicates that small changes in demand result in larger price changes.

When the US experienced an increase in hairstyle demand, the price adjustment was significantly larger due to its steeper supply curve slope of \(20\). This contrasts with France’s more moderate slope of \(6.67\), meaning demand shifts there result in less dramatic price changes.

Thus, the statement "The impact of an increase in demand depends critically on the slope of the supply curve" holds true. In general:

• A steeper supply slope suggests restricted producer flexibility, leading to more substantial price hikes when demand grows.
• A flatter slope indicates greater flexibility, with prices affected less by the same demand increase.

Understanding supply curve slope assists in predicting market reactions to changes in demand, aiding businesses and policymakers in decision-making processes.