Question

Question 1: The demand function of the peanut butter market is given as Qp=40-2P, and the market equilibrium price is $10. (25%) I. If the price increased to $11, compute the (point) elasticity at $10 II. Compute the arc elasticity between $10 and $11. III. If the price increased to $15, compute the (point) elasticity at $10, and the arc elasticity between $10 and $15. Is the point elasticity different from your previous answer? IV. The average income of the neighborhood increased from $50,000 to $60,000. We observe the peanut butter sales dropped from 20 to 16 units. Compute the income elasticity of peanut butter. (When not specified, you should compute the point elasticity) V. What type of good is peanut butter given its income elasticity? Question 2: In a perfectly competitive market, the demand curve is given as: Q=100-5P, the supply curve is given as Q=3P-12. (30%) I. Compute the total social surplus of this market. II. If the government impose a tax on the producers, and the tax rate is $2 per unit produced. Graphically show the tax revenue and the deadweight loss (DWL). III. Compute the new producer surplus and the DWL. IV. Instead of taxing the producers, if the government impose the same tax ($2 per unit) on the consumers, graphically show the change in the market equilibrium and the DWL. V. Does it really matter whether the tax is imposed on consumers or the producers?

Answer 1

The point elasticity of demand at a price of $10 when the price increases to $11 is -1.

To calculate the point elasticity of demand, we can use the formula:

Elasticity = (Percentage change in quantity demanded) / (Percentage change in price)

The point elasticity at a price of $10 when the price increases to $11:

The initial quantity demanded (Q1) at a price of $10 using the demand function: Q1 = 40 - 2 * 10 = 20

The new quantity demanded (Q2) at a price of $11: Q2 = 40 - 2 * 11 = 18

The percentage change in quantity demanded:

Percentage Change in Quantity Demanded = (Q2 - Q1) / Q1 * 100

⇒ (-2 / 20) * 100 = -10%

The percentage change in price: Percentage Change in Price = (New Price - Old Price) / Old Price * 100

⇒ (11 - 10) / 10 * 100 = 10%

Apply the elasticity formula: Elasticity = Percentage Change in Quantity Demanded / Percentage Change in Price

⇒ -10% / 10% = -1

Therefore, the point elasticity of demand at a price of $10 when the price increases to $11 is -1.

Answer 2

The point elasticity of demand at a price of $10 when the price increases to $11 is -1.

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)

We will use this to compute the point elasticity of demand at a price of $10 when the price increases to $11.

The initial quantity demanded (Q1) at a price of $10 using the demand function:

Q1 = 40 - 2 * 10

Q1 = 40 - 20

Q1 = 20

The new quantity demanded (Q2) at a price of $11:

Q2 = 40 - 2 * 11

Q2 = 40 - 22

Q2 = 18

The percentage change in quantity demanded:

= [(Q2 - Q1) / Q1] * 100

= [(18 - 20) / 20] * 100

= (-2 / 20) * 100

= -10%

The percentage change in price:

= [(New Price - Old Price) / Old Price] * 100

= [(11 - 10) / 10] * 100

= (1 / 10) * 100

= 10%

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)

Elasticity = (-10% / 10%)

Elasticity = -1.