Final answer:
By setting the demand equation, Qd = 16 - 2P, equal to the supply equation, Qs = 2 + 5P, and solving for P, we find the equilibrium price P* to be 2. Substituting P* into either equation yields the equilibrium quantity Q* as 12. Additionally, the equilibrium level of output Y is given as $10,000.
Step-by-step explanation:
To derive the equilibrium price, P*, and quantity, Q*, we begin by setting the demand equation equal to the supply equation because at equilibrium, quantity demanded (Qd) equals quantity supplied (Qs). The given equations are Qd = 16 - 2P and Qs = 2 + 5P. By setting them equal to each other, we get 16 - 2P = 2 + 5P.
To solve for P, we rearrange the terms: 16 - 2 = 5P + 2P, which simplifies to 14 = 7P. Therefore, the equilibrium price is P* = 2. Substituting back into one of the original equations gives us the equilibrium quantity: Q* = 2 + 5(2) = Q* = 12.
Regarding the equilibrium level of output, Y, the given equation is Y = $500 + 0.8(Y - T) + $2000 + $1000 + $2000 - 0.05(Y - T) which simplifies to Y = $10,000. This represents the total economic output at equilibrium.