(a) How is equilibrium level of output determined under short run?
(b) How is it derived?

Equilirium Output. Output is at its equilibrium level when quantity of output produced (AS) is equal to quantity demanded (AD). The economy is in equilibrium when aggregate demand represented by C + I is equal to total output.
(a) Determination of Equilibrium level of output
Under short run fixed price, equilibrium level of output is determined solely by level of ex-ante aggregate demand. How? To keep the explanation of theory simple, certain assumptions are made. (I) Prices of final goods are assumed to be constant (fixed) in short run because the economy takes time to respond to forces of excess supply or demand.
(ii) Theory is applicable under only short run. (iii) Supply is perfectly elastic, which means at given price suppliers are willing to supply whatever amount of goods consumers will demand, (iv) It is a two-sector (Household and Firms) economy assuming no government and foreign trade.
Under such circumstances, in short run (when supply is infinitely elastic at constant price) equilibrium output will be solely determined by aggregate amount of demand at that price in the economy. This is known as effective demand principle. Aggregate supply is relatively a passive force in determining level of output in short run. Now the question is how is aggregate demand at fixed price derived.

(b) Derivation of equilibrium output and Aggregate demand.
At short run fixed price value of ex-ante aggregate demand is equal to sum of consumption expenditure and investment expenditure i.e., AD = C + I. Under effective demand principle, equilibrium outnut or aggregate supply(Y) is equal to aggregate demand (AD), i.e.. Y = AD. Again Y is represented bv equation 
This is further simplified as under:
               

Equilibrium output and equilibrium demand at fixed price and constant rate of interest is derived by solving the equation, 
Clearly value of equilibrium output Y will depend on values of  and b. Let us illustrate it with a numerical example. Suppose values of autonomous expenditure are  and value of b = 0.8. What will be equilibrium value of output Y?

Y = 375 is the equilibrium output of the economy at fixed price and fixed interest rate combination.