U=(q1q2)0,5 Y= 70 p1=4$ p2=9$ P1 increases to 9$ calculate the compensation variation.

U=(q₁q₂)^0,5

Y= 70

p₁=4$ p₂=9$

P₁ increases to 9$ calculate the compensation variation.

Solutions

Expert Solution

Compensating variation is the amount of compensation given to the consumer so that initial bundle remain just affordable or the level of utility to the consumer remain same.

Compensating variation= Change in price x intial optimal quantity of the good whose price changes

U=(q₁q₂)^0.5

U= q₁^0.5 q₂^0.5

Budget line: 4q₁ +9q₂ = 70

Marginal utility of q₁ (MUq₁ )= Differentiation of U wrt q₁ = 0.5q₁^-0.5 q₂^0.5

Marginal utility of q₂ (MUq₂ )= Differentiation of U wrt q₂ = 0.5q₂^-0.5 q₁^0.5

MRS= (MUq₁ )/(MUq₂ )= q₂ /q₁

Slope of budget line= p₁/p₂=4/9

Optimal condition:

MRS= Slope of budget line

q₂ /q₁ = 4/9

9q₂ = 4q₁ Equation 1

Use this equation in budget line:

4q₁ +4q₁ = 70

8q₁ = 70

q₁* = 70/8 (intial optimal quantity of the good whose price changes)

Now P₁ increases to 9$:

Compensating variation= Change in price x q₁*

Compensating variation= (9-4) (70/8)= 5 x (70/8)= 350/8= 175/4= 43.75

Income should be compensated by $43.75 so that initial bundle can still be just affordable.

Rahul Sunny answered 1 year ago

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