9. Use the information provided here for Questions 9 to 11:  Douglas’s demand function for good x is x(px,py,m)=2m/5px. His income is $1,000, the price of x is $5, and the price of y is $20. If the price of x falls to $4, then his demand for x will______________.

Select one:

a.

change from 80 to 100

b.

not change

c.

change from 100 to 90

d.

Need more information

To solve this, we will use Douglas’s demand function for good $ x $, which is:

\[
x(p_x, p_y, m) = \frac{2m}{5p_x}
\]

Where:
- $ p_x $ is the price of good $ x $,
- $ p_y $ is the price of good $ y $,
- $ m $ is Douglas's income.

### Step 1: Initial demand for $ x $ when $ p_x = 5 $
Given:
- $ m = 1000 $,
- $ p_x = 5 $,
- $ p_y = 20 $ (though it doesn't affect the demand for $ x $).

Using the demand function:

\[
x(5, 20, 1000) = \frac{2 \times 1000}{5 \times 5} = \frac{2000}{25} = 80
\]

So, the initial demand for $ x $ when the price of $ x $ is 5 is **80**.

### Step 2: New demand for $ x $ when $ p_x = 4 $
Now, if the price of $ x $ falls to 4:

\[
x(4, 20, 1000) = \frac{2 \times 1000}{5 \times 4} = \frac{2000}{20} = 100
\]

So, the new demand for $ x $ when the price of $ x $ is 4 is **100**.

### Conclusion:
The demand for good $ x $ changes from 80 to 100 when the price of $ x $ falls from 5 to 4.

Therefore, the correct answer is:

**a. change from 80 to 100**

Would you like further details or have any questions?

---

Here are 5 related questions to consider:
1. What happens to the demand if the price of $ y $ changes?
2. How does income $ m $ affect Douglas’s demand for $ x $?
3. What is the relationship between demand and the price elasticity of demand?
4. How would the demand change if both $ p_x $ and $ m $ change simultaneously?
5. What is the significance of the coefficient $ \frac{2}{5} $ in the demand function?

**Tip:** The demand function suggests that the demand for a good is inversely proportional to its price—meaning that as price decreases, demand generally increases.

Douglas’s demand function for good x is x(px,py,m)=2m/5px. His income is $1,000, the price of x is $5, and the price of y is $20. If the price of x falls to $4, then his demand for x will______________. Select one: a. change from 80 to 100 b. not change c. change from 100 to 90 d. Need more information

Explore how Douglas's demand for good x changes as the price of x decreases from $5 to $4. Using the demand function x(px, py, m) = 2m / 5px, we calculate the demand for x when income is $1,000 and px changes. Learn about key concepts in microeconomics, such as the law of demand and price elasticity.

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