In: Economics
Consider an economy consisting of 11 people, 10 citizens and their mayor. the mayor is choosing whether to implement a sales tax, t, on the good x1 or an income tax, r, on each citizens salary. Suppose each good x1 and x2 has the common respective price of 1. Furthermore, each citizen receives an income of $10,000 and all citizens have the same utility preferences given by: U (x1, x2 ) = √x1 √x2
What is the budget constraint in the case of having an income tax r and the second constraint when consumers face the sales tax t.
Using those budget constraints solve for the demand functions under each tax regime. Then calculate the tax rate needed so the mayor receives a salary equal to the same $10,000 the rest of the citizens receive.
What criteria would the mayor use to then choose whether to implement the sales or income tax? Which one should the mayor choose and why?
Budget constraint (income tax r) ----(1)
x1 + x2 = 10000 -r
Budget constraint (sales tax t) ------(2)
x1 + x2 = 10000 - t
Utility function U(x1,x2) = (x1x2)^1/2
Under each tax regime, the consumer would want to maximize utility.
Undet tax regime of income tax r
Lagrange equation => L = U +
FOC => and
x2 = x1
substitute in budget constraint
x1 = (10000-r)/2 x2 =(10000- r)/2
Mayor should get salary 10000 = income tax collected in total
10 citizens are charged 1000 each so that mayor gets 10000.
income tax rate is 10 percent.
r = 1000
Under tax regime of sales tax t per unit x1
x2= (1+t)x1
x1 = 5000/(1+t)
x2 = 5000
Mayor receives 10000 = tx1* 10
50000t/(1+t) = 10000
t = 1/4
Mayor should adopt the tax regime whichc maximises utility of the citizens.
In case of income tax
x1 = 4500, x2= 4500
u = (4500*4500)^1/2 = 4500
In case of sales tax per unit
x1 = (5000*4000)^1/2 = 4472
'Therefore income tax regime should be adopted.