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### a) Elasticidad precio de la demanda (método del punto medio)
We are asked to calculate the price elasticity of demand using the midpoint method for the price change from $8 to $10, both for an income of $10,000 and $12,000.

The formula for price elasticity of demand using the midpoint method is:
\[
E_d = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}
\]
Where:
- $P_1$ and $P_2$ are the initial and final prices.
- $Q_1$ and $Q_2$ are the initial and final quantities demanded.

#### i) For an income of $10,000:
- $P_1 = 8$, $P_2 = 10$
- $Q_1 = 40$, $Q_2 = 32$

Applying the formula:
\[
E_d = \frac{\frac{32 - 40}{(32 + 40)/2}}{\frac{10 - 8}{(10 + 8)/2}} = \frac{\frac{-8}{36}}{\frac{2}{9}} = \frac{-8}{36} \times \frac{9}{2} = -1
\]

#### ii) For an income of $12,000:
- $P_1 = 8$, $P_2 = 10$
- $Q_1 = 50$, $Q_2 = 45$

Applying the formula:
\[
E_d = \frac{\frac{45 - 50}{(45 + 50)/2}}{\frac{10 - 8}{(10 + 8)/2}} = \frac{\frac{-5}{47.5}}{\frac{2}{9}} = \frac{-5}{47.5} \times \frac{9}{2} = -0.474
\]

### b) Elasticidad ingreso de la demanda (método del punto medio)
Now, we calculate the income elasticity of demand for a change in income from $10,000 to $12,000. The formula for income elasticity is:
\[
E_i = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{I_2 - I_1}{(I_2 + I_1)/2}}
\]
Where:
- $I_1$ and $I_2$ are the initial and final incomes.
- $Q_1$ and $Q_2$ are the quantities demanded at those income levels.

#### i) When the price is $12:
- $I_1 = 10,000$, $I_2 = 12,000$
- $Q_1 = 24$, $Q_2 = 30$

Applying the formula:
\[
E_i = \frac{\frac{30 - 24}{(30 + 24)/2}}{\frac{12,000 - 10,000}{(12,000 + 10,000)/2}} = \frac{\frac{6}{27}}{\frac{2,000}{11,000}} = \frac{6}{27} \times \frac{11,000}{2,000} = 1.22
\]

#### ii) When the price is $16:
- $I_1 = 10,000$, $I_2 = 12,000$
- $Q_1 = 8$, $Q_2 = 12$

Applying the formula:
\[
E_i = \frac{\frac{12 - 8}{(12 + 8)/2}}{\frac{12,000 - 10,000}{(12,000 + 10,000)/2}} = \frac{\frac{4}{10}}{\frac{2,000}{11,000}} = \frac{4}{10} \times \frac{11,000}{2,000} = 2.2
\]

### Summary:
- Price elasticity of demand (income = $10,000): $E_d = -1$
- Price elasticity of demand (income = $12,000): $E_d = -0.474$
- Income elasticity of demand (price = $12): $E_i = 1.22$
- Income elasticity of demand (price = $16): $E_i = 2.2$

Would you like further clarification or more details on any of these steps?

Here are 5 related questions for deeper understanding:
1. How does price elasticity vary with different income levels?
2. What does a negative price elasticity value indicate about the product's demand?
3. How would the elasticity calculations change if the price increased to $14?
4. What is the significance of the midpoint method in elasticity calculations?
5. How do different income elasticity values affect market demand predictions?

**Tip:** Always remember that price elasticity helps businesses understand how sensitive consumers are to price changes, which can guide pricing strategies.

Utilice el método del punto medio para calcular la elasticidad precio de la demanda cuando el precio de la palta aumenta de $8 a $10, y calcule la elasticidad ingreso de la demanda cuando el ingreso aumenta de $10,000 a $12,000.

Learn how to calculate price elasticity of demand when the price changes from $8 to $10, and income elasticity when income increases from $10,000 to $12,000. This problem covers key economic concepts including the midpoint method for elasticity.

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