## To solve this problem, let's break it down step by step:

a) The demand function is given as:

Qd = 1,800 - 20P + 0.6M - 50Pr

In this scenario, income (M) is $19,500 and the price of the related good (Pr) is $250. To find the initial demand curve D2, we need to substitute these values into the demand function.

Qd2 = 1,800 - 20P + 0.6(19,500) - 50(250)

Qd2 = 1,800 - 20P + 11,700 - 12,500

Qd2 = -9,000 - 20P

Now, let's move on to the next part of the question.

b) If there is a decrease in income causing consumers to be willing and able to purchase 300 fewer units at each price, we need to find the new demand curve D3.

To find the equation for D3, we subtract 300 from the previous demand curve, Qd2.

Qd3 = -9,000 - 20P - 300

Qd3 = -9,300 - 20P

Now, let's analyze the last part of the question.

c) We need to determine by how much income must fall to cause the shift from D2 to D3.

To find the change in income, we need to compare the coefficients of M in the demand equations.

Coefficient of M in D2 = 0.6

Coefficient of M in D3 = 0 (as it's not present in the equation)

Therefore, income must fall by 0.6 * 19,500 = $11,700 for the shift from D2 to D3.

To summarize:

a) D2 equation: Qd2 = -9,000 - 20P

b) D3 equation: Qd3 = -9,300 - 20P

c) Income must fall by $11,700 for the shift from D2 to D3.