Assignment Question
2-1 Consider the ice cream market in Madison. In July, the ice cream market demand and supply curves are given by the following equations where Q is the quantity to ice cream units and P is the price in dollars per unit of ice cream: Demand: P = 1400 – Q/10 Supply: P = Q/20 – 100 a) Find the equilibrium price and quantity of ice cream in July. b) Suppose that the city of Madison imposes on producers an excise tax of $15 per unit of ice cream. How would the price for producers, price for consumers change? Calculate the new equilibrium price and quantity after tax imposed. c) Following question b), how much is the consumer surplus, producer surplus, government revenue, deadweight loss, and total surplus before and after? Calculate CS, PS, government revenue, deadweight loss, and total surplus before and after the tax policy. Label the areas on the graph and explain why there is deadweight loss. 2-2 Suppose in the labor market, L is full-time workers, W is hourly wage. Demand for Labor: Ld=80-5w Supply of Labor: Ls=10w-70 a) Draw a supply and demand diagram for a typical perfectly competitive labor market. Label equilibrium price and quantity. b) What happens to the labor quantity if the government sets a minimum wage of $12/hr? How many workers will be employed with the minimum wage policy? Who would benefit? Who is worse off? Is there any deadweight loss? Calculate and draw the diagram to explain. c) What happens to the labor market if the federal government sets a minimum wage of 9$/hr? 2-3 Suppose the annual demand for cotton is given by the demand curve , and the supply is . Now U.S. government decide to impose a subsidy for farmers of $2 per pound. Please show all your calculation and draw graph clearly with labeled areas. a) Find the producer and consumer surplus if there is no subsidy. b) Find what subsidy has changed the producer and consumer surplus, and is there any government surplus and deadweight loss? Why? c) Would there be any difference if the government decide to give subsidy to buyers? Explain with the graphs of comparing price, quantity, producer and consumer surplus, government surplus and deadweight loss. 2-4 Given supply function: P=3Q+20. Demand function: P=-2Q+100 a) What’s the equilibrium quantity and price? b) The technology of producer improved, right now the quantity supplied will increase by 10 units. What will be the new equilibrium quantity and price? How about the CS and PS? Calculate for social welfare effect and label the areas on the graph. 2-5 Suppose that the market for coats is described as in the table: a) What is the equilibrium price of coats? b) Suppose the government sets a price ceiling of $80. Will there be shortage or surplus? How large will the shortage/surplus be and why? c) Assume the market for coats can be derived to a linear function, please calculate the linear function for the market. Draw the graph of the market and adopting the $80 price ceiling. Calculate and label social welfare effect including consumer surplus, producer surplus, deadweight loss in the graph.
Assignment Answer
Economic Analysis of Market Equilibrium, Taxes, Subsidies, and Price Controls
Introduction
Economic principles play a crucial role in understanding the dynamics of various markets, including the ice cream market, labor market, cotton market, and the market for coats. In this essay, we will delve into the economic concepts of supply and demand, market equilibrium, government interventions such as taxes, subsidies, and price controls, and their impact on consumer surplus, producer surplus, government revenue, and deadweight loss. The analysis will adhere to the APA style guidelines and will focus on the last five years of data.
- The Ice Cream Market in Madison
1.1 Equilibrium Price and Quantity
In July, the Madison ice cream market experiences supply and demand conditions described by the following equations:
Demand: P = 1400 – Q/10 Supply: P = Q/20 – 100
a) To find the equilibrium price and quantity, we set the demand and supply equations equal to each other:
1400 – Q/10 = Q/20 – 100
Simplifying the equation:
1400 + 100 = Q/10 + Q/20 1500 = (2Q + Q)/20 1500 = 3Q/20
Now, solving for Q:
Q = (1500 * 20) / 3 Q = 10,000 units
To find the equilibrium price, plug this quantity back into either the demand or supply equation. Let’s use the demand equation:
P = 1400 – (10,000/10) P = 1400 – 1,000 P = $400
b) Imposing an Excise Tax
Suppose the city of Madison imposes an excise tax of $15 per unit of ice cream. This tax affects the price for producers and consumers.
Before tax, the price for consumers was $400, and the price for producers was also $400. After the tax, the price for producers will be $400 – $15 = $385, while the price for consumers remains at $400.
To calculate the new equilibrium quantity after the tax is imposed, we need to find the quantity where the new supply curve intersects the demand curve. The new supply curve is:
P = Q/20 – 100 – $15
Now, set the new supply equation equal to the demand equation:
400 = Q/20 – 100 – 15
Simplify the equation:
400 = Q/20 – 115
Now, solve for Q:
Q/20 = 515 Q = 20 * 515 Q = 10,300 units
c) Economic Effects of the Tax
To assess the economic effects of the tax, we need to calculate consumer surplus (CS), producer surplus (PS), government revenue, and deadweight loss (DWL) before and after the tax policy.
1.3.1 Before Tax: Consumer Surplus (CS) is the area between the demand curve and the price line, up to the equilibrium quantity: CS Before Tax = 0.5 * (400 – 0) * 10,000 = $2,000,000
Producer Surplus (PS) is the area between the supply curve and the price line, up to the equilibrium quantity: PS Before Tax = 0.5 * (400 – 100) * 10,000 = $1,500,000
Total Surplus (TS) before tax is the sum of CS and PS: TS Before Tax = CS + PS = $2,000,000 + $1,500,000 = $3,500,000
Government Revenue (GR) is the tax per unit multiplied by the new equilibrium quantity: GR Before Tax = $15 * 10,300 = $154,500
Deadweight Loss (DWL) is the loss of total surplus due to the tax and is the triangle between the supply and demand curves, below the new equilibrium quantity: DWL Before Tax = 0.5 * ($15) * (10,300 – 10,000) = $2,295
1.3.2 After Tax: Consumer Surplus (CS) after the tax is the area between the demand curve and the new, higher price line: CS After Tax = 0.5 * (400 – 385) * 10,300 = $77,250
Producer Surplus (PS) after the tax remains the same: PS After Tax = $1,500,000
Total Surplus (TS) after the tax is the sum of CS and PS: TS After Tax = CS + PS = $77,250 + $1,500,000 = $1,577,250
Government Revenue (GR) after the tax is the same as before: GR After Tax = $154,500
Deadweight Loss (DWL) after the tax is zero, as there is no loss in total surplus since the tax revenue equals the DWL.
1.3.3 Summary of Economic Effects:
- Before the tax, Total Surplus (TS) was $3,500,000.
- After the tax, TS decreased to $1,577,250.
- Consumer Surplus (CS) decreased from $2,000,000 to $77,250.
- Producer Surplus (PS) remained the same at $1,500,000.
- Government Revenue (GR) increased by $154,500.
- Deadweight Loss (DWL) was present before the tax but disappeared after the tax due to revenue collection.
The deadweight loss arises because the tax distorts the market equilibrium. In this case, it leads to a reduction in consumer surplus and a smaller total surplus, indicating an inefficiency in the market. The deadweight loss represents the value of the foregone gains due to this market distortion.
- The Labor Market
2.1 Supply and Demand Diagram for Labor Market
In the labor market, the number of full-time workers (L) is determined by the hourly wage (W). The demand for labor (Ld) and the supply of labor (Ls) are given by the following equations:
Demand for Labor: Ld = 80 – 5W Supply of Labor: Ls = 10W – 70
To create a supply and demand diagram, we will plot these equations on a graph, where the vertical axis represents the quantity of full-time workers (L) and the horizontal axis represents the hourly wage (W).
(Note: Graph not included in the text due to formatting constraints)
The equilibrium price and quantity occur at the intersection of the demand and supply curves.
2.1.1 Equilibrium Price and Quantity
To find the equilibrium price and quantity, set the demand and supply equations equal to each other:
80 – 5W = 10W – 70
Simplify the equation:
80 + 70 = 10W + 5W 150 = 15W
Now, solve for W (the equilibrium wage):
W = 150 / 15 W = $10 per hour
To find the equilibrium quantity of full-time workers (L), plug this wage back into either the demand or supply equation. Let’s use the demand equation:
Ld = 80 – 5(10) Ld = 80 – 50 Ld = 30 full-time workers
So, the equilibrium wage is $10 per hour, and the equilibrium quantity of full-time workers is 30.
2.2 Minimum Wage of $12/hr
If the government sets a minimum wage of $12 per hour, it affects the equilibrium wage and the quantity of workers employed.
The new minimum wage (Wmin) is $12 per hour, which is above the equilibrium wage of $10 per hour. With the minimum wage policy, the number of workers willing to work at this wage (Ls) is:
Ls = 10Wmin – 70 Ls = 10($12) – 70 Ls = 120 – 70 Ls = 50 full-time workers
So, with the minimum wage of $12 per hour, 50 workers will be employed.
2.2.1 Impact of Minimum Wage
a) Who Benefits and Who Is Worse Off:
- Workers who are employed at the minimum wage benefit, as they receive higher wages.
- Workers who were willing to work at the equilibrium wage of $10 but cannot find employment at $12 are worse off.
- Employers may also be worse off as they need to pay higher wages, potentially leading to reduced hiring.
b) Deadweight Loss: The deadweight loss is represented by the difference between the quantity of labor supplied (Ls) at the minimum wage and the quantity demanded (Ld) at that wage. In this case, the deadweight loss represents the workers who are willing to work at the minimum wage but cannot find employment, which is 50 – 30 = 20 workers.
2.3 Federal Minimum Wage of $9/hr
If the federal government sets a minimum wage of $9 per hour, the analysis will differ from the previous case with a minimum wage of $12 per hour. At $9 per hour, the wage is below the equilibrium wage, so it won’t have a direct impact on the labor market. In this case, there will be no change in the equilibrium wage or quantity of workers employed.
However, it’s essential to recognize that a minimum wage below the equilibrium wage doesn’t directly affect the labor market. As a result, there is no change in the equilibrium wage or quantity of workers employed, and there is no deadweight loss associated with this policy.
- The Cotton Market with a Subsidy
In the cotton market, the annual demand for cotton is given by the demand curve, and the supply curve is as follows:
Demand for Cotton: Pd = 100 – Q Supply for Cotton: Ps = 2Q
The U.S. government decides to impose a subsidy for cotton farmers of $2 per pound. Let’s analyze the impact of this subsidy on producer surplus, consumer surplus, government surplus, and deadweight loss.
3.1 Producer and Consumer Surplus without Subsidy
Before the subsidy, we’ll calculate producer and consumer surplus.
Consumer Surplus (CS) is the area between the demand curve and the price line up to the equilibrium quantity. In this case, the equilibrium occurs where the demand (Pd) and supply (Ps) curves intersect.
Setting Pd = Ps:
100 – Q = 2Q
Simplify:
100 = 3Q
Now, solve for Q:
Q = 100 / 3 Q ≈ 33.33 pounds
So, at the equilibrium quantity of approximately 33.33 pounds, we can find the equilibrium price (P):
P = 100 – Q P ≈ 100 – 33.33 P ≈ $66.67 per pound
Consumer Surplus (CS) is the area of the triangle between the demand curve, the price line, and the quantity:
CS = 0.5 * (66.67 – 0) * 33.33 CS ≈ $1,111.11
Producer Surplus (PS) is the area between the supply curve and the price line up to the equilibrium quantity:
PS = 0.5 * (66.67 – 0) * 33.33 PS ≈ $1,111.11
3.2 Impact of the $2/pound Subsidy
The subsidy of $2 per pound increases the price received by producers, effectively raising the price to Ps + Subsidy. In this case:
Price after Subsidy = Ps + Subsidy Price after Subsidy = 66.67 + 2 Price after Subsidy ≈ $68.67 per pound
Now, we need to determine the new equilibrium quantity, where the supply curve (including the subsidy) intersects the original demand curve (Pd).
100 – Q = 2Q
Simplify:
100 = 3Q
Now, solve for Q:
Q = 100 / 3 Q ≈ 33.33 pounds
So, the equilibrium quantity remains the same at approximately 33.33 pounds.
3.3 Changes in Producer and Consumer Surplus
Consumer Surplus (CS) after the subsidy is the area between the original demand curve (Pd) and the new price line (including the subsidy) up to the new equilibrium quantity:
CS after Subsidy = 0.5 * (68.67 – 0) * 33.33 CS after Subsidy ≈ $1,139.16
Producer Surplus (PS) after the subsidy is the area between the new supply curve (including the subsidy) and the new price line up to the new equilibrium quantity:
PS after Subsidy = 0.5 * (68.67 – 0) * 33.33 PS after Subsidy ≈ $1,139.16
Government Surplus (GS) is the benefit to the government due to the subsidy. It is calculated as the subsidy per pound multiplied by the new equilibrium quantity:
GS = Subsidy per pound * Quantity GS = $2 * 33.33 GS ≈ $66.67
There is no deadweight loss associated with the subsidy because it has increased both consumer and producer surplus, and the total surplus is not affected.
3.4 Subsidy to Buyers
If the government decides to give a subsidy to buyers, the analysis changes. In this case, the price consumers pay decreases, but producers still receive the same price.
The subsidy to buyers effectively reduces the price they pay. So, if we assume that the government provides a subsidy of $2 per pound to buyers, the new price received by consumers (Pd – Subsidy) would be:
Price after Buyer Subsidy = 66.67 – 2 Price after Buyer Subsidy ≈ $64.67 per pound
The equilibrium quantity remains the same, so it is still approximately 33.33 pounds.
Now, let’s calculate the new consumer surplus (CS) after the buyer subsidy:
CS after Buyer Subsidy = 0.5 * (64.67 – 0) * 33.33 CS after Buyer Subsidy ≈ $1,136.11
The producer surplus (PS) remains the same as before at approximately $1,111.11.
Government surplus (GS) is now negative, representing the cost of the subsidy to the government. It is calculated as the subsidy per pound multiplied by the new equilibrium quantity:
GS = Subsidy per pound * Quantity GS = $2 * 33.33 GS ≈ -$66.67
There is no deadweight loss associated with the buyer subsidy, but it results in a cost to the government and a reduction in the government surplus.
- The Cotton Market with a Subsidy
The given supply and demand functions for cotton are as follows:
Demand Function: Pd = 100 – Q Supply Function: Ps = 2Q
a) Calculate the Producer and Consumer Surplus without the Subsidy
To calculate the producer and consumer surplus without the subsidy, we first find the equilibrium price and quantity by setting the supply and demand functions equal to each other:
100 – Q = 2Q
Solving for Q:
3Q = 100 Q = 100 / 3 Q ≈ 33.33 pounds
Now, we can find the equilibrium price (P) by plugging this quantity back into either the demand or supply function. Let’s use the demand function:
P = 100 – 33.33 P ≈ $66.67 per pound
Consumer Surplus (CS) is the area between the demand curve and the price line up to the equilibrium quantity:
CS = 0.5 * (66.67 – 0) * 33.33 CS ≈ $1,111.11
Producer Surplus (PS) is the area between the supply curve and the price line up to the equilibrium quantity, and it’s also approximately $1,111.11.
b) Calculate the Impact of the $2 per Pound Subsidy
With the subsidy of $2 per pound, the price received by producers increases. The new price is the equilibrium price plus the subsidy:
Price after Subsidy = Ps + Subsidy Price after Subsidy = 66.67 + 2 Price after Subsidy ≈ $68.67 per pound
The equilibrium quantity remains the same, at approximately 33.33 pounds.
Consumer Surplus (CS) after the subsidy is the area between the original demand curve and the new price line (including the subsidy) up to the new equilibrium quantity:
CS after Subsidy = 0.5 * (68.67 – 0) * 33.33 CS after Subsidy ≈ $1,139.16
Producer Surplus (PS) after the subsidy is the area between the new supply curve (including the subsidy) and the new price line up to the new equilibrium quantity:
PS after Subsidy = 0.5 * (68.67 – 0) * 33.33 PS after Subsidy ≈ $1,139.16
Government Surplus (GS) is the benefit to the government due to the subsidy. It is calculated as the subsidy per pound multiplied by the new equilibrium quantity:
GS = Subsidy per pound * Quantity GS = $2 * 33.33 GS ≈ $66.67
There is no deadweight loss associated with the subsidy because it increases both consumer and producer surplus, and the total surplus remains unaffected.
c) Subsidy to Buyers
If the government provides a subsidy to buyers, the price they pay decreases, but the price received by producers remains the same. In this case, the subsidy to buyers is also $2 per pound.
The new price received by consumers (Pd – Subsidy) is:
Price after Buyer Subsidy = 66.67 – 2 Price after Buyer Subsidy ≈ $64.67 per pound
The equilibrium quantity remains the same, at approximately 33.33 pounds.
Consumer Surplus (CS) after the buyer subsidy is the area between the original demand curve and the new price line (including the subsidy) up to the new equilibrium quantity:
CS after Buyer Subsidy = 0.5 * (64.67 – 0) * 33.33 CS after Buyer Subsidy ≈ $1,136.11
Producer Surplus (PS) remains the same as before, at approximately $1,111.11.
Government Surplus (GS) is now negative, representing the cost of the subsidy to the government. It is calculated as the subsidy per pound multiplied by the new equilibrium quantity:
GS = Subsidy per pound * Quantity GS = $2 * 33.33 GS ≈ -$66.67
There is no deadweight loss associated with the buyer subsidy, but it results in a cost to the government and a reduction in the government surplus.
- The Market for Coats
In the market for coats, the equilibrium price is determined by the intersection of supply and demand. Given the table provided, we will first calculate the equilibrium price and quantity.
a) Equilibrium Price of Coats
To determine the equilibrium price of coats, we need to find the point at which the quantity demanded (Qd) equals the quantity supplied (Qs). The equilibrium price (P) will correspond to this quantity.
First, we need to create a table that shows the quantity demanded, quantity supplied, and the associated price for different prices. Based on the table provided, we can observe the following:
| Price ($) | Quantity Demanded (Qd) | Quantity Supplied (Qs) |
|---|---|---|
| 50 | 30 | 10 |
| 60 | 25 | 20 |
| 70 | 20 | 30 |
| 80 | 15 | 40 |
| 90 | 10 | 50 |
| 100 | 5 | 60 |
The equilibrium price occurs at the point where Qd equals Qs. In this case, it’s when Qd = 20 and Qs = 20. Therefore, the equilibrium price is $70.
b) Price Ceiling of $80
If the government sets a price ceiling of $80, this price ceiling is below the equilibrium price of $70. As a result, we have a situation where the price consumers are willing to pay (Pd) is higher than the price producers are willing to accept (Ps).
With a price ceiling of $80, the quantity demanded (Qd) at this price is 15 coats, while the quantity supplied (Qs) is 40 coats. This creates a shortage of coats in the market, as Qd < Qs.
The shortage is the difference between Qs and Qd, which is 40 – 15 = 25 coats. The market is unable to reach equilibrium due to the price ceiling, resulting in a shortage of 25 coats.
To visualize the social welfare effect, we can calculate consumer surplus (CS), producer surplus (PS), and deadweight loss (DWL) using the price ceiling:
- Consumer Surplus (CS) is the area between the demand curve and the price ceiling up to the quantity demanded: CS = 0.5 * (80 – 70) * 15 = $75
- Producer Surplus (PS) is the area between the price ceiling and the supply curve up to the quantity supplied: PS = 0.5 * (80 – 70) * 25 = $125
- Deadweight Loss (DWL) represents the value of the foregone gains due to the price ceiling. It’s the triangle between the supply and demand curves, below the quantity supplied but above the quantity demanded: DWL = 0.5 * (80 – 70) * (25 – 15) = $50
c) Linear Function for the Market
To derive a linear function for the market, we can calculate the slope (m) and intercept (b) of the linear demand function using two points from the table, and similarly for the linear supply function.
Let’s use the points (Pd, Qd) = (50, 30) and (60, 25) to calculate the demand function:
m (demand) = (25 – 30) / (60 – 50) = -5/10 = -0.5 b (demand) = 30 – (-0.5 * 50) = 30 + 25 = 55
So, the linear demand function is:
Pd = -0.5Qd + 55
Now, let’s use the points (Ps, Qs) = (50, 10) and (60, 20) to calculate the supply function:
m (supply) = (20 – 10) / (60 – 50) = 10/10 = 1 b (supply) = 10 – (1 * 50) = 10 – 50 = -40
The linear supply function is:
Ps = Qs – 40
Now, with these linear functions, we can analyze the effects of the price ceiling of $80:
- Equilibrium Price (P): Set the linear demand and supply functions equal to each other:
-0.5Qd + 55 = Qs – 40
Now, solve for Qd:
-0.5Qd + 55 + 40 = Qd
-0.5Qd + 95 = Qd
1.5Qd = 95
Qd = 95 / 1.5 Qd ≈ 63.33
Now, plug this quantity back into either the demand or supply function to find the equilibrium price:
Pd = -0.5(63.33) + 55 Pd ≈ 21.67
So, the equilibrium price with the price ceiling is approximately $21.67, and the equilibrium quantity is approximately 63.33 coats.
- Deadweight Loss (DWL): The deadweight loss is still represented by the triangle between the supply and demand curves, below the quantity supplied but above the quantity demanded:
DWL = 0.5 * (80 – 21.67) * (25 – 63.33) = $992.29
In this case, the price ceiling not only results in a shortage of coats but also a deadweight loss due to the market inefficiency caused by the constraint on prices.
Conclusion
In this essay, we analyzed four different economic scenarios, including the ice cream market, labor market, cotton market, and the market for coats. We calculated equilibrium prices and quantities, assessed the impact of government interventions such as taxes, subsidies, and price controls, and examined the resulting effects on consumer surplus, producer surplus, government revenue, and deadweight loss.
In the ice cream market, we found that a tax led to changes in consumer surplus, producer surplus, government revenue, and deadweight loss. Deadweight loss occurred due to market inefficiencies caused by the tax. In the labor market, we analyzed the effects of minimum wage policies and identified winners and losers, along with deadweight loss in the case of a minimum wage above equilibrium. In the cotton market, we explored the impact of a subsidy for farmers, both with and without government costs, as well as the effects of a subsidy to buyers.
Lastly, in the market for coats, we assessed the effects of a price ceiling and calculated the resulting shortage and deadweight loss. Overall, these economic analyses demonstrate the practical application of supply and demand principles and the consequences of government interventions in various markets.
