Question

John considers milk (x1) and hot chocolate (x2) to be perfect substitutes at a rate of 2 : 1, that is, he always receives the same utility if he has two glasses of milk or one cup of hot chocolate to drink. He spends $12 a day on hot beverage, and milk cost $1 while hot chocolate cost $3 each.

1. Draw the Income Offer Curve and Engel Curve for milk.

2. Draw the Price Offer Curve and Demand Curve for milk.

3. The price of hot chocolate decreases to $1, and his income and the price of milk dont change. How does consumption change when the price of hot chocolate changes? What is John’s new level of utility? Show your result on a graph.

4. How much must John’s budget decrease to return him to the original utility level?

Answer 1

It is given that substitutes x₁ (milk) and x₂ (hot chocolate) are substitutes and the rate is 2:1, that is, 2 units of x₁ is equal to 1 unit of x₂. Thus, the utility function is (x₁+ 2x₂). This is because a utility function depicts the combination of x₁ and x₂ that results in a constant level of utility.

It is given that the money income is $12 and the price of x₁ and x₂ is $1 and $3 respectively.

The slope of budget constraint is = - ( price of x₁)/ (price of x₂) = - (1/3)

The Marginal rate of substitution (MRS) is computed as -

It can be concluded that the MRS is greater than the slope budget constraint. That is, consumer, spends all his income on consumption of good x₁.

The income offer curve (IOC) and the Engel curve is shown below -

The Price offer curve (POC) and the Demand curve is shown below -

The price of hot chocolate (p2) falls from to $3 to $1. The optimal quantity is computed as -