A system of equations is given by:

F1(x,y,a,b) = x² + bxy + y² - a – 2 = 0
F2(x,y,a,b) = x² + y ² - b² + 2a + 3 = 0

Where x and y are endogenous variables while a and b are exogenous variables. Compute the differentials δx/δb and δy/δa at the point (x,y,a,b) = (0,1,3,4)

To compute the differentials δx/δb and δy/δa at the given point (x, y, a, b) = (0, 1, 3, 4) for the given system of equations, we need to take partial derivatives of each equation with respect to the specified variables.

Let's start with finding δx/δb:

1. Take the partial derivative of the first equation F1(x, y, a, b) with respect to b while treating a and y as constants.
∂F1/∂b = (2xy) + (xy)

2. Plug in the given values (x, y, a, b) = (0, 1, 3, 4) into the derivative we obtained:
∂F1/∂b = (2 * 0 * 1) + (0 * 1)
= 0 + 0
= 0

Therefore, δx/δb = 0.

Next, let's compute δy/δa:

1. Take the partial derivative of the second equation F2(x, y, a, b) with respect to a while treating x and b as constants.
∂F2/∂a = 2(x) + 0

2. Plug in the given values (x, y, a, b) = (0, 1, 3, 4) into the derivative we obtained:
∂F2/∂a = 2 * (0) + 0
= 0 + 0
= 0

Therefore, δy/δa = 0.

So, the differentials δx/δb and δy/δa at the point (x, y, a, b) = (0, 1, 3, 4) are both equal to 0.