/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 The market for whisky in Scotlan... [FREE SOLUTION] | 91Ó°ÊÓ

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The market for whisky in Scotland is described by the following demand and supply equations: Demand: \(Q^{D}=80-P\) Supply: \(Q^{S}=-40+2 P\) where \(P\) is the price of a liter of whisky and \(Q\) is the number of liters sold per week, in thousands. Suppose the Scottish government mandates a price of \(£ 60\) per liter. a. Is the market in equilibrium? Why or why not? b. At the government's price, is there an excess demand or excess supply of whisky? c. Suppose that the government decides to let the price of whisky be determined by the market rather than by the government. Based on your answer to (b), would you expect the price of whisky to increase, decrease, or stay the same? Explain your reasoning intuitively.

Short Answer

Expert verified
The market is not in equilibrium at £60; there is an excess supply of 60,000 liters, and the price will decrease if allowed to adjust freely.

Step by step solution

01

Determine Equilibrium Conditions

First, we need to find the equilibrium price and quantity, which occurs when demand equals supply. Set the demand equation equal to the supply equation: \(80-P = -40+2P\).
02

Solve for Equilibrium Price

Rearrange the equation from Step 1 to solve for the equilibrium price \(P\):\[\begin{align*}80 - P &= -40 + 2P \80 + 40 &= 2P + P \120 &= 3P \P &= \frac{120}{3} = 40\end{align*}\]The equilibrium price \(P\) is £40.
03

Solve for Equilibrium Quantity

Substitute the equilibrium price \(P = 40\) into either the demand or supply equation to find the equilibrium quantity \(Q\). Using the demand equation: \(Q^{D} = 80 - 40 = 40\). Thus, the equilibrium quantity \(Q\) is 40,000 liters.
04

Compare Government Price with Equilibrium Price

The equilibrium price is £40, but the government mandates a price of £60. Since £60 is higher than the equilibrium price, the market is not in equilibrium.
05

Determine Excess Supply or Demand

Calculate the quantities demanded and supplied at the government's price of £60:- Demand: \(Q^{D} = 80 - 60 = 20\)- Supply: \(Q^{S} = -40 + 2  60 = 80\)Since \(Q^{S} (80) > Q^{D} (20)\), there is an excess supply of 60,000 liters.
06

Predict Market Outcome if Price is Determined by Market

With an excess supply at £60, suppliers will compete to sell their whisky, which will drive down the price. Hence, if the government allows market forces to determine the price, the price of whisky will decrease toward the equilibrium price of £40.

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Key Concepts

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

Supply and Demand
Supply and demand are fundamental concepts that describe how goods and services are allocated in a market.
The concept centers around the interaction between sellers (supply) and buyers (demand). These interactions determine the price and quantity of a good sold.
A demand equation specifies how much of a product consumers are willing to buy at varying prices. For example, the demand for whisky in Scotland is expressed as \( Q^{D} = 80 - P \), where \( P \) represents the price per liter and \( Q \) the quantity in thousands of liters.
The supply equation shows how much producers are willing to sell at different prices, as demonstrated by \( Q^{S} = -40 + 2P \).
When the quantity demanded equals the quantity supplied, the market is in equilibrium. This means that at a specific price, known as the equilibrium price, the amount of whisky consumers want to buy matches the amount suppliers are willing to sell.
  • **Equilibrium Price:** The price at which supply meets demand.
  • **Equilibrium Quantity:** The quantity sold at the equilibrium price.
The process of setting these equations equal allows businesses and economists to determine those exact values. In our exercise, the equilibrium price is £40, which means that at this price, 40,000 liters of whisky are traded each week.
Understanding supply and demand is crucial as it is the backbone of market operations.
Price Controls
Price controls are government-imposed limits on the prices that can be charged for goods and services in a market. These include price ceilings and price floors.
In the scenario of the whisky market in Scotland, the government sets a price floor at £60 per liter.
This floor is above the market's natural equilibrium price of £40.
When price floors are implemented above the equilibrium price, it can lead to a misallocation of resources as the market is not allowed to adjust freely.
  • **Price Ceiling:** A legal maximum on the price at which a good can be sold.
  • **Price Floor:** A legal minimum on the price at which a good can be sold.
Price controls are used with good intentions, such as stabilizing markets or protecting consumers and producers from rapid price fluctuations.
However, they may lead to unintended consequences like surpluses or shortages, as traders are driven by market forces.
In the case of the whisky market, the price floor led to a situation where producers had more supply (80,000 liters) than consumers were willing to buy (20,000 liters) at the fixed price.
Excess Supply and Demand
Excess supply and demand occur when there is a misalignment between the quantity supplied and the quantity demanded at a given price.
In the whisky market exercise, a government-mandated price of £60 results in excess supply.
Excess supply, also known as a surplus, happens when producers are supplying more of a product than consumers are willing to purchase. In this exercise, 80,000 liters were supplied, but only 20,000 liters wanted.
This leads to a surplus of 60,000 liters.
Conversely, excess demand, or a shortage, occurs when demand exceeds supply at a given price.
Understanding these concepts is vital to predict how a market will react when external factors such as government interventions change the equilibrium.
  • **Excess Supply:** When quantity supplied exceeds quantity demanded.
  • **Excess Demand:** When quantity demanded exceeds quantity supplied.
If the price is set too high, as with the whisky example, producers will either have to reduce the price to a more competitive rate or find alternative markets.
Lifting the price control allows the market to self-correct, eventually adjusting to balance supply and demand, typically reducing prices toward the equilibrium point.

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Most popular questions from this chapter

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