Consider A Market Where Supply And Demand Are Given By 10 An

10consider A Market Where Supply And Demand Are Given By 10 And

10. Consider a market where supply and demand are given by = -10+ and = 56 -. Suppose the government imposes a price floor of $25, and agrees to purchase any and all units consumers do not buy at the floor price of $25 per unit. a. Determine the cost to the government of buying firms’ unsold units. b. Compute the lost social welfare (deadweight loss) that stems from the $25 price floor. 1

Paper For Above instruction

Introduction

In economic theory, price floors are a form of government intervention aimed at supporting prices to benefit producers, typically in markets where prices fall below a desirable threshold. However, such interventions can lead to market distortions, excess supply, and social welfare losses, known as deadweight loss. This paper examines a specific case where the supply and demand functions are given, and a price floor of $25 is implemented, analyzing the associated costs and welfare impacts in detail. We will evaluate the cost incurred by the government in purchasing unsold units and quantify the deadweight loss resulting from the price floor, illustrating these concepts through clear calculations.

Market Equilibrium and Specifications

Given the supply and demand functions:

- Supply function: \( Q_s = -10 + P \)

- Demand function: \( Q_d = 56 - P \)

The market equilibrium occurs where supply equals demand:

\[

-10 + P = 56 - P

\]

Solving for \( P \):

\[

2P = 66 \Rightarrow P_e = 33

\]

At equilibrium, the quantity is:

\[

Q_e = -10 + 33 = 23

\]

Thus, the natural market equilibrium price is $33 with a corresponding quantity of 23 units.

Impact of the Price Floor

The government imposes a price floor of $25, which is below the equilibrium price. Since a price floor is effective only when set above the equilibrium price, in this case, the price floor of $25 is non-binding; market equilibrium remains at $33, and the market operates unaffected by the floor.

However, for the purpose of this analysis, let us consider the scenario as if the price floor were binding (for illustrative purposes), perhaps if it were set at a level where the demand exceeds supply at that price, and the government agrees to purchase all unsold units. Assume we interpret the problem under a hypothetical binding price floor at $25, leading to excess supply or unsold units.

Note: Since the original problem states that the price floor is $25 and the government agrees to purchase unsold units, it implicitly suggests the price floor is effective and may cause distortions. We will proceed under the assumption that at $25, the market's reduced demand and supply create unsold units, and the government’s purchase impacts welfare.

Calculating Unsold Units and Government Cost

At the price floor \( P_f = 25 \):

- Quantity supplied: \( Q_s = -10 + 25 = 15 \)

- Quantity demanded: \( Q_d = 56 - 25 = 31 \)

Since supply is only 15 units at this price, but demand is 31 units, there is no excess supply; demand exceeds supply, and no unsold units.

However, if the price floor were set above the equilibrium price (say, at $35), then supply and demand would be:

- \( Q_s = -10 + 35 = 25 \)

- \( Q_d = 56 - 35 = 21 \)

In this case, supply exceeds demand, leading to surplus units:

\[

\text{Surplus} = Q_s - Q_d = 25 - 21 = 4

\]

The government agrees to buy all unsold units at the price floor. The total cost to the government is:

\[

\text{Cost} = \text{Surplus units} \times \text{Price} = 4 \times 35 = \$140

\]

Thus, the government spends $140 to purchase the excess units.

Summary:

- At the actual price floor of $25, there are no unsold units; government cost is zero.

- If the price floor is set above the equilibrium (e.g., $35), the government incurs a cost of $140 for surplus units.

Calculating Deadweight Loss

Deadweight loss (DWL) occurs from the reduction in trade volume due to the price floor, leading to inefficiencies.

At equilibrium:

- Quantity: 23 units

- Price: $33

With a binding price floor at, say, $35:

- Quantity supplied: 25 units

- Quantity demanded: 21 units

- Surplus units: 4 units

The DWL is the loss of welfare from these 4 units not traded due to the price floor. The deadweight loss is represented as the triangle between supply and demand curves:

\[

\text{DWL} = \frac{1}{2} \times \text{Surplus units} \times (\text{Price difference})

\]

where:

\[

\text{Price difference} = P_{supply} - P_{demand}

\]

However, since the demand and supply functions are linear, the exact DWL is calculated based on the change in quantity and the difference in their respective prices at those quantities.

Alternatively, using the standard approach:

\[

\text{DWL} = \frac{1}{2} \times (\text{Quantity reduction}) \times (\text{Price distortion})

\]

The reduction in traded quantity due to the price floor is from 23 units to 21 units, so:

\[

\text{Quantity reduction} = 2

\]

The price difference between equilibrium ($33) and the price floor ($35), which causes the quantity reduction, is \$2.

Thus:

\[

\text{DWL} = \frac{1}{2} \times 2 \times 2 = 2

\]

measured in welfare units.

Conclusion:

The deadweight loss attributable to the binding price floor set at $35 is valued at 2 welfare units, representing the lost gains from trade due to market distortions.

Conclusion

In markets where a government sets a price floor above the equilibrium price, there are significant economic consequences, including costs from purchasing surplus units and deadweight loss associated with reduced transactions. Accurate calculations depend on the exact level of the price floor relative to the equilibrium. When set above the equilibrium, these interventions can lead to substantial inefficiencies, testing the delicate balance in market regulation strategies.

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