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Let's break down part (a) and solve it step by step.

**Problem:**
A 20% increase in the price of Product A causes a 10% decrease in its quantity demanded, but no change in the quantity demanded of Product B.

We are asked to calculate the **cross-price elasticity** of demand between Product A and Product B. The formula for cross-price elasticity is:

\[
\text{Cross-price elasticity} = \frac{\%\ \text{change in quantity demanded of Product B}}{\%\ \text{change in price of Product A}}
\]

### Step 1: Identify the values
- % change in price of Product A = 20% (increase)
- % change in quantity demanded of Product B = 0% (no change)

### Step 2: Apply the values to the formula
Since the quantity demanded of Product B does not change, we have:

\[
\text{Cross-price elasticity} = \frac{0\%}{20\%} = 0
\]

### Step 3: Interpret the result
The cross-price elasticity is **0**, which means that the demand for Product B does not change in response to changes in the price of Product A. Hence, the relationship between Product A and B is that they have **no relationship** (they are neither complements nor substitutes).

### Final Answer:
- Cross-price elasticity between A and B: **0**
- Relationship between A and B: **no relationship**

Would you like any further details or clarification on this? 

Here are 5 related questions to expand your understanding:
1. What is the cross-price elasticity when products are substitutes?
2. How does the cross-price elasticity differ when products are complements?
3. Can a cross-price elasticity ever be negative? What does that imply?
4. Why would two products have no relationship in terms of cross-price elasticity?
5. How can cross-price elasticity affect pricing strategies in the market?

**Tip:** Cross-price elasticity helps firms understand how a change in the price of one good can affect the demand for another, which is crucial for competitive and complementary product pricing strategies.

A 20% increase in the price of Product A causes a 10% decrease in its quantity demanded but no change in the quantity demanded of Product B.

Calculate the cross-price elasticity between Product A and Product B where a 20% increase in price of Product A leads to no change in the demand for Product B. This problem helps understand the relationship between products based on elasticity concepts.

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