Question

1. Modou has a utility function U(X₁,X₂) = 2X₁ + X₂

The prices of X₁ & X₂ are $1 each and Modou has an income of $20 budgeted for this two goods.

1. Draw the demand curve for X₁ as a function of p₁.
2. At a price of p₁ = $1, how much X₁ and X₂ does Modou consume?
3. A per unit tax of $0.60 is placed on X₁. How much of good X₁ will he consume now?
4. Suppose the government decides to combine this with a lump-sum subsidy that makes Modou as well-off as he was before the tax. With this new income, how much of X₁ will Modou demand? How much is the subsidy?
5. Based on you answer to d) what are the Income and Substitution effects of the original per-unit tax on X₁?

Answer 1

A) utility Maximizing condition,

mUx1/px1=MUx2/px2

2/1>1/1

So per $ MU from x1 is more than per $ MU from x2 and it is fixed . And the goods are perfect substitues ,so given per $ MU of x1 is more than x2 , CONSUMER will spend all his income on x1.

X1=20/1=20

At px1=2

MUx1/px1=2=MUx2/px2

Px1 above 2 make demand of x1 zero because then the per $ MU from x1 will be lower than per $ MU from X2.

B) as explained in part a) x1=20 and x2=0

C) A tax of 0.6 on x1 ,will make price of x1 =1+0.6=1.6

With new price optimal bundle consumption condition,

2/1.6>1/1

1.25>1,

Still per $ MU from x1 is greater than per $ MU from X2, and given both goods are perfect substitue so, CONSUMER spend his entire income on x1

X1=20/1.6=12.5

C) so to be better as before ,it means modou can buy. Same quantity as before which was equal to 20.

So income required to buy 20 units of x1 with new price=20*1.6=32

So subsidy=32-20=12

X1=20

E) as due to change in relative price of x1 and x2 ,there is no change in relative demand of x1 and x2 g( x2 is still zero)utility level .so substitution effect is zero. And entire income effect is equal to price effect.