Question 1178454
Let's break down this demand equation problem step-by-step:

**(a) Expressing the Equation as a Relationship Between QD(G) and p(G)**

Given:
* QD(G) = 7.5 - 0.5p(G) + 0.1(I) - 0.5P(A)
* I = $60
* P(A) = $30

Substitute the values of I and P(A) into the equation:

QD(G) = 7.5 - 0.5p(G) + 0.1(60) - 0.5(30)
QD(G) = 7.5 - 0.5p(G) + 6 - 15
QD(G) = 7.5 + 6 - 15 - 0.5p(G)
QD(G) = -1.5 - 0.5p(G)

So, the equation relating quantity demanded of gasoline (QD(G)) to its price (p(G)) is:

**QD(G) = -0.5p(G) - 1.5**

**(b) Calculating the Y-intercept**

The Y-intercept is the value of QD(G) when p(G) = 0.

Substitute p(G) = 0 into the equation:

QD(G) = -0.5(0) - 1.5
QD(G) = -1.5

Therefore, the Y-intercept is **-1.5**.

**(c) Showing an Inward Shift with Income Change**

Now, let's change the income (I) to $50, while keeping P(A) constant at $30.

Substitute I = $50 and P(A) = $30 into the original equation:

QD(G) = 7.5 - 0.5p(G) + 0.1(50) - 0.5(30)
QD(G) = 7.5 - 0.5p(G) + 5 - 15
QD(G) = 7.5 + 5 - 15 - 0.5p(G)
QD(G) = -2.5 - 0.5p(G)

So, the new equation is:

**QD(G) = -0.5p(G) - 2.5**

**Comparison:**

* Original equation (I = $60): QD(G) = -0.5p(G) - 1.5
* New equation (I = $50): QD(G) = -0.5p(G) - 2.5

**Explanation:**

1.  **Parallel Shift:** Notice that the slope (-0.5) remains the same in both equations. This indicates that the new demand curve is parallel to the original demand curve.
2.  **Y-intercept Change:** The Y-intercept has changed from -1.5 to -2.5. This means that for any given price, the quantity demanded is now lower.
3.  **Inward Shift:** Since the Y-intercept has decreased, the entire demand curve has shifted downward (inward) on the graph. This shift represents a decrease in demand at every price level due to the decrease in income.
4.  **Not a Movement Along the Curve:** A movement along the demand curve would only occur if the price of gasoline (p(G)) changed. Since the price of gasoline remains a variable in the equation and the income changed, the whole curve shifts.

**Conclusion:**

The decrease in household income from $60 to $50 results in an inward shift of the demand curve for gasoline. This shows that a change in income, a non-price determinant of demand, causes a shift of the demand curve, not a movement along it.