Question

Thomas buys tomatoes, T, and cucumbers, C, from a local grocery store. Thomas has 10 dollars in his pocket, and his utility function is given by U(T, C) = T · C. An owner of the store is a weird person who does not like customers buying an equal amount of vegetables and, as a result, he came up with an unusual pricing scheme. In particular, a customer who buys more cucumbers than tomatoes is charged 2 dollars for each tomato and only 1 dollar for each cucumber. However, those who buy more tomatoes than cucumbers are charged 2 dollars for each cucumber and only 1 dollar for each tomato. Finally, in case somebody buys the same amount of cucumbers and tomatoes, the price of each vegetable is 2 dollars.

1. Draw the budget constraint for Thomas if he decides to buy more tomatoes than cucumbers.

2. Draw the budget constraint for Thomas if he decides to buy more cucumbers than tomatoes.

3. Find the optimal combination of tomatoes and cucumbers Thomas will choose. Graphical Solution would suffice!

Answer 1

Let cucumber be good 1 (denoted by x₁) and tomatoes be good 2 (denoted by x₂).

1) if he decides to buy more tomatoes than cucumbers, then he is charged 2 dollars for each cucumber and only 1 dollar for each tomato.

Price of tomato (p₂) = $1

Price of cucumber (p₁) = $2

The budget line in this case is given by:

p₁x₁ + p₂x₂ = M

2x₁ + x₂ = 10

When x₁ = 0 units, then x₂ = 10 units. This is the y-intercept.

When x₂ = 0 units, then x₁ = 5 units. This is the x-intercept.

The budget line has been drawn in figure 1.

Figure 1

2)  if he decides to buy more cucumbers than tomatoes, he is charged 2 dollars for each tomato and only 1 dollar for each cucumber.

Price of tomato (p₂) = $2

Price of cucumber (p₁) = $1

The budget line in this case is given by:

p₁x₁ + p₂x₂ = M

x₁ + 2x₂ = 10

When x₁ = 0 units, then x₂ = 5 units. This is the y-intercept.

When x₂ = 0 units, then x₁ = 10 units. This is the x-intercept.

The budget line has been drawn in figure 2.

Figure 2

3) Now, if he buys more more tomatoes, he faces budget line 1. If he buys more cucumber, he faces budget line 2. His final budget line has been highlighted in green in figure 3.

The required garphis given below. The IC has been drawn in red color. The consumer is equally well off consuming 2.5 cucmbers and 5 tomatoes or 5 cucmbers and 2.5 tomatoes

Figure 3