Suppose there are 8,000 identical individuals in a market for Latin Dance videos

Question

Suppose there are 8,000 identical individuals in a market for Latin Dance videos, each with a demand function represented by Qdx=12-2Px, and 400 identical producers of Latin Dance videos, each with a supply function of Qsx=10Px.

- What is the market demand and market supply function for Latin Dance videos?

- How do I obtain the market equilibrium price and quantity using algebra?

-Derive the market demand and market supply schedule for dance videos at prices ranging from $1 to $6 and sketch the market demand and market supply curves and label the equilibrium price and quantity.

- Use the Demand equation to find the price elasticity of demand. Is the price elasticity demand elastic or in elastic?


- Interpret the elasticity of demand and state by how much quantity in demand would fall if price for dance videos would increase by 2%.

Explanation / Answer

Suppose there are 8,000 identical individuals in a market for Latin Dance videos, each with a demand function represented by Qdx=12-2Px, and 400 identical producers of Latin Dance videos, each with a supply function of Qsx=10Px.

- What is the market demand and market supply function for Latin Dance videos?

- How do I obtain the market equilibrium price and quantity using algebra?

-Derive the market demand and market supply schedule for dance videos at prices ranging from $1 to $6 and sketch the market demand and market supply curves and label the equilibrium price and quantity.

- Use the Demand equation to find the price elasticity of demand. Is the price elasticity demand elastic or in elastic?


- Interpret the elasticity of demand and state by how much quantity in demand would fall if price for dance videos would increase by 2%. quantity demanded = 8000*(12-2px) = 96000 - 16000px
Supply: 400*(10PX) = 4000PX

Equilibrium occurs when Quantity demanded = quantity supplied

96000 - 16000PX = 4000PX
96000 = 20000PX
96000/20000 = PX = 4.8
Now that we have the price we can insert it into the demand function to find the number of units.

96000 - 16000*4.8 = 96000 - 76000 = 20000 units demanded.

For the market demand and supply schedule just insert the price into the equation so for $1
Demand = 96000 - 16000*1 = 80000
Supply = 4000 * 1 = 4000
Excess demand = 76000

Point elasticity of demand = P/Q * DQ/DP(derivative of quantity with respect to P)

4.8/20000 * -16000 = -3.84
Ed = 0 Perfectly inelastic demand
- 1 < Ed < 0 Inelastic or relatively inelastic demand
Ed = - 1 Unit elastic, unit elasticity, unitary elasticity, or unitarily elastic demand
- 8 < Ed < - 1 Elastic or relatively elastic demand
Ed = - 8 Perfectly elastic demand

Since -3.84 falls under elastic demand, we can determine that it is elastic.
If prices increase by 2% demand would change by -3.84*2% = -7.68%

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.