Given a demand curve of P = 196 - 4Qd and supply of P = 10 + 2Qs, find the total cost to society of a lump sum tax of 13 dollars, assuming the government is as efficient in resouce use as households.
To find the total cost to society of a lump-sum tax of $11, we need to analyze the impact of the tax on the demand and supply sides of the market. This can be done by following these steps:
First, let's find the equilibrium price and quantity without the tax. Equilibrium occurs when the quantity demanded (Qd) equals the quantity supplied (Qs).
So, we can set the demand and supply equations equal to each other:
Demand (D): P = 103 - 1Qd
Supply (S): P = 31 + 7Qs
Setting D = S
103 - 1Qd = 31 + 7Qs
Now, we can solve for Qd and Qs
1Qd + 7Qs = 103 - 31
1Qd + 7Qs = 72
Now, we have a system of two equations with two unknowns:
1Qd + 7Qs = 72
P = 103 - 1 Qd
We need to solve these equations simultaneously. We'll use the first equation to find Qd and Qs:
1Qd = 103 - 7Qs
Qd = (103 - 1(72 - 7 Qs))
Now, substitute this Qd value into the second equation to find P:
P = 103 -72 + 7 Qs
P = 31 + 7Qs
So, at the initial equilibrium, Qd = (72 - 7Qs) and P = 31 + 7Qs.
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