Chapter 9, Problem 9.8P

a)

To determine

To calculate: The following:

1. Short-run supply curve for each snuffbox maker
2. Short-run supply curve for the market as a whole

Answer to Problem 9.8P

1. Short-run supply curve for each snuffbox maker is $\boxed{P=q+10}$
2. Short-run supply curve for the market as a whole is $\boxed{Q_s=100P-1,000}$

Explanation of Solution

Given:

Total identical firms $=100$

Short-run total cost $STC=0.5q^2+10q+5$

Short-run marginal cost $SMC=q+10$

Explain:

1. In the perfect competition, supply curve for each firm will be equal to its short-run marginal cost.

Thus, the short-run supply curve for each snuffbox market is $P=q+10$

2. As there are 100 firms in the industry thus industry supply is given as follows:

  $Q_s=100q$

  $q=P-10$

  $=100\left(P-10\right)$

  $=100P-1,000$

Economics Concept Introduction

Introduction: One of the portion in the marginal cost that will appear above its average variable cost curve is defined as short-run supply curve. Suppose if the market price rises, the firm will supply more of that particular product.

b)

To determine

To Calculate: The following:

1. Equilibrium in the market
2. Each firm’s total short-run profit

Answer to Problem 9.8P

1. Equilibrium in the market is $\boxed{\$14}$
2. Each firm’s total short-run profit is $\boxed{\$3}$

Explanation of Solution

Given:

  $Q=1,100-50P$

Explain:

a)

For equilibrium demand must be equal to its supply

  $Q_s=100P-1,000$

  $Q_d=1,100-50P$

Calculate the equilibrium as follows:

Set $Q_d=Q_s$

  $100P-1,000=1,100-50P$

  $150P=2,100$

  $\boxed{P=14}$

b)

Calculate the equilibrium quantity as follows:

Substitute the value of P in the equation to get the value of Q.

  $Q_d=1,100-50P$

  $=1,100-50\times 14$

  $=1,100-700$

  $=\boxed{400units}$

Thus, the equilibrium quantity is $\boxed{400units}$

As there are 100 firms, each firm will produce $\frac{400}{100}=4units$

The formula for calculating total profit as follows:

  $\text{Profit=TR-TC}$

Calculate TC as follows:

  $STC=0.5q2+10q+5$

  $=0.5\times 16+10\times 4+5$

  $=8+40+5$

  $=\boxed{53}$

Thus, the firms total cost is $\boxed{53}$

Calculate the firm’s total revenue as follows:

  $TR=P\times q$

  $=14\times 4$

  $=\boxed{56}$

Thus, the total revenue is $\boxed{\$56}$

Calculate the total profit as follows:

  $SR=TR-TC$

  $=\left(\left(4\times 14\right)-\left(8+40+5\right)\right)$

  $=56-53$

  $=3$

Thus, the firms total short run profit is $\boxed{\$3}$

Economics Concept Introduction

Introduction: Equilibrium is one of the market price where supplied goods is similar to the demanded goods. In this place only demand and supply curves in the market intersect. During market equilibrium, the supply and demand meet in a specific price.

c)

To determine

To Graph: The market equilibrium and compute total producer surplus in this case.

Answer to Problem 9.8P

  

Total producer surplus is $\boxed{\$2,400}$

Explanation of Solution

In the graph, quantity is represented on the horizontal axis and price on the vertical axis.

Equilibrium is at the point where demand and supply curve intersect each other.

Thus, the equilibrium price is $\boxed{\$14}$ and quantity is $\boxed{400units}$

Calculate the consumer surplus as follows:

Consumer surplus $=\frac{1}{2}\text{base}\times \text{height}$

  $\text{=}\frac{1}{2}\left(400-0\right)\left(22-14\right)$

  $=\frac{1}{2}\times 400\times 8$

  $=\boxed{\$1,600}$

Thus, the consumer surplus is $\boxed{\$1,600}$

Calculate the producer surplus as follows:

Producer surplus $=\frac{1}{2}\text{base}\times \text{height}$

  $\text{=}\frac{1}{2}\left(400-0\right)\left(14-10\right)$

  $=\frac{1}{2}\times 400\times 4$

  $=\boxed{\$800}$

Thus, the Producer surplus is $\boxed{\$800}$

Calculate the total surplus as follows:

Total surplus=Consumer surplus +Producer surplus

  $=\$1,600+\$800$

  $=\boxed{\$2,400}$

Thus, the total surplus is $\boxed{\$2,400}$

Economics Concept Introduction

Introduction: There is a great demand and equal supply, the markets are at equilibrium during summer. During post summer season, the supply will start falling and demand will remain the same. The corresponding price is the equilibrium price, also the quantity is the equilibrium quantity.

d)

To determine

To Show: The calculated total producer surplus in part c is equal to total industry profits plus industry short-run fixed costs.

Answer to Problem 9.8P

Total producer surplus is $\boxed{\$800}$

Total industry profits and industry short-run fixed costs is $\boxed{\$800}$

Therefore, the total industry profits plus industry short-run fixed cost is equal to producer’s surplus.

Explanation of Solution

Calculate the total profits of the industry as follows:

Total profit of the industry $=3\times 100$

  $=\boxed{\$300}$

Thus, the total profit of the industry is $\boxed{\$300}$

Calculate the short run fixed costs as follows:

  $SRFC=5\times 100$

  $=\boxed{500}$

Thus, the short run fixed cost is $\boxed{500}$

Because as per the equation, $STC=0.5q^2+10q+5$ the fixed costs is the constant number.

Sum up both the total profit and short run fixed cost as follows:

Total profits+SRFC $=300+500$

  $=\boxed{800}$

Thus, it equals to $\boxed{\$800}$

The producer surplus is $\boxed{\$800}$ (Computed in Part b).

Economics Concept Introduction

Introduction: Fixed costs are the expenditures that does not change based on the levels of production at least not in the short term. The fixed costs are same when the product will be produced a lot or little.

e)

To determine

To calculate: The tax change the market equilibrium when the government imposed a $3 tax on snuffboxes.

Answer to Problem 9.8P

The market equilibrium price has declined from $14 to $13 and also the equilibrium quantity has declined by $100(from 400 to 300 units)

Explanation of Solution

Because of tariffs, new demand curve will be $Q=1,100-50\left(P+3\right)$

  $Q_d=1,100-50P-150$

  $=950-50P$

  $Q_s=100P-1,000$

Calculate the new equilibrium price as follows:

  $950-50P=100P-1,000$

  $150=1,950$

  $P+3=16$

  $P=\boxed{\$13}$

Thus, the equilibrium price is $\boxed{\$13}$

Calculate the equilibrium quantity as follows:

  $Q_s=100P-1,000$

  $=100\times 13-1,000$

  $=1,300-1,000$

  $=\boxed{300units}$

Thus, the equilibrium quantity is $\boxed{300units}$

Economics Concept Introduction

Introduction: Demanded quantity will be similar to the supplied quantity in a particular price is defined as Equilibrium. Suppose if the tax will be imposed by the government into the market, the tax imposed is to impact of the equilibrium. If the tax increases the price a buyer pays less than the tax.

f)

To determine

To Describe: The burden of the tax to be shared between snuffbox buyers and sellers.

Answer to Problem 9.8P

Tax paid is $\boxed{\$900}$

Consumers and producers will pay $\boxed{\$600}$ and $\boxed{\$300}$ respectively.

Explanation of Solution

Calculate the tax paid as follows:

Tax paid $=3\times 300$

  $=\boxed{\$900}$

Economics Concept Introduction

Introduction: Tax burden is divided between buyers and sellers. Suppose if the supply is more elastic than demand, buyers bear most of the tax burden. Otherwise, if the demand is more elastic than supply, producers bear most of the tax burden.

g)

To determine

To Calculate: The total loss of producer surplus as a result of the taxation of snuffboxes.

Answer to Problem 9.8P

The total loss of producer surplus as a result of the taxation of snuffboxes are $\boxed{\$350}$

Explanation of Solution

Calculate the producer surplus as follows:

Produce surplus $=\frac{1}{2}\text{base}\times \text{height}$

  $\text{=}\frac{1}{2}\left(13-10\right)\times 300$

  $=\boxed{450}$

Thus, the producer surplus is $\boxed{\$450}$

Calculate the total loss of producer’s surplus as a result of the taxation of snuffboxes as follows:

Total loss $=800-450$

  $=\boxed{\$350}$

Economics Concept Introduction

Introduction: The difference between prices is that Producers are willing to sell a product based on their costs within price and market equilibrium price is defined as produce surplus. Suppose if the economy produces the inefficient quantity, total surplus will occur. Deadweight is loss in the total producer.