Question

QUESTION 20

1. Mandy gets utility from consuming nutella and doritos. Her utility function is of the following form:

   U = 50 Doritos + 87 Nutella
   
   The price of nutella is $63 per jar, the price of doritos is $16 per bag and her income is $3,931
   
   What is the MRS(doritos, nutella)?

QUESTION 21

1. The utility function and the prices are the following:
   
   U =min{ 80 x₁ , 12 x₂}
   
   P₁=50,   P₂=52 and I =5,157
   
   What is the optimal amount of x₂?

Answer 1

Question 20:

U = 50 Doritos + 87 Nutella

MRS (doritos, Nutella) = -(Marginal utility of Doritos / Marginal Utility of Nutella)

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U = 50 Doritos + 87 Nutella

Marginal utility of Doritos = ΔU / ΔDoritos.

Marginal utility of Doritos = 50

and

Marginal utility of Nutella = ΔU / ΔNutella

=> Marginal utility of Nutella = 87

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MRS (doritos , Nutella) = -(Marginal utility of Doritos / Marginal Utility of Nutella)

=> MRS (doritos , Nutella) = - (50 / 87)

=> MRS (doritos , Nutella) = -0.57

Answer: -0.57

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Question 21:

U = min [80x₁, 12x₂]

The above utility function states that good x₁ and x₂ are complements goods.

Price of good x₁ (P₁) = 50

Price of good x₂ (P₂) = 52

and

Income (I) = 5157.

Budget constraint: x₁ *P₁ + x₂*P₂ = I

=> 50x₁ + 52x₂ = 5157

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U = min [80x₁, 12x₂]

Since good x₁ and x₂ are complements goods.

In case of complements goods, utility will maximized at following point;

80x₁ = 12x₂

=> x₁ = (12x₂ / 80)

=> x₁ = 0.15x₂ -------------------- eq(1)

Put eq(1) in budget constraint:

50x₁ + 52x₂ = 5157

=> 50 (0.15x₂) + 52x₂ = 5157

=> 7.5x₂ + 52x₂ = 5157

=> 59.5x₂ = 5157

=> x₂ = (5157 / 59.5)

=> x₂ = 86.67

Answer: The optimal amount of x₂ is 86.67