Answer :
To find the equilibrium level of national income, we use the concept of aggregate demand equaling aggregate supply in an economy. The components given are the consumption function [tex]C = 100 + 0.75Y[/tex] and investment [tex]I = 1000[/tex].
In equilibrium, aggregate demand equals national income ([tex]Y[/tex]). Therefore, we express this as:
[tex]Y = C + I[/tex]
Substituting the given functions into this equation:
[tex]Y = (100 + 0.75Y) + 1000[/tex]
First, we simplify and rearrange the equation:
[tex]Y = 100 + 0.75Y + 1000[/tex]
[tex]Y = 1100 + 0.75Y[/tex]
Subtracting [tex]0.75Y[/tex] from both sides to isolate [tex]Y[/tex]:
[tex]Y - 0.75Y = 1100[/tex]
[tex]0.25Y = 1100[/tex]
Now, solve for [tex]Y[/tex] by dividing both sides by 0.25:
[tex]Y = \frac{1100}{0.25}[/tex]
[tex]Y = 4400[/tex]
However, none of the options directly include 4400, so we should revisit the steps. On a closer inspection of given values or options, we notice a possible misunderstanding in provided choices. Ensure the calculations were correctly interpreted, as sometimes exercise options might not match the recalculated values based on similar exercises.
Thus, based on the methodology of equilibrium calculation, it can be concluded through the context of exercise options or review if there's unique mapping but in this exercise's main solution basis, calculated value would have been approximately larger size than available options.
Using the computed equilibrium national income methodologically, option 'd) 3700' could mistakenly appear in close rough differences, due to untracked minutiae if occurred observationally during exercise provision. However, based on mathematical foundation presented, equilibrium didn't tightly align particularly here directly without recognized model's fine comparison check or alternate intents.
