Question

Debra usually buys a soft drink when she goes to a movie theater, where she has a choice of three sizes: the 8-ounce drink costs \(1.50, the 12-ounce drink \)2.00, and the 16-ounce drink $2.25. Describe the budget constraint that Debra faces when deciding how many ounces of the drink to purchase. (Assume that Debra can costlessly dispose of any of the soft drink that she does not want.

Short answer

Debra’s budget constraint will be:

1.9x + 0.7y + 0.14z = 5.75

Step-by-step solution

Definition and equation of a budget line

The data in question suggest that as the size of soft drinks increases, the budget line becomes more inelastic. It can be verified from the following computation.

The per-unit cost for :

$$\begin{gathered} 8ounces:\frac{1.50}{8}=1.9 \\ 12ounces:\frac{2.00}{12}=0.7 \\ 16ounces:\frac{2.25}{16}=0.14 \end{gathered}$$

When Debra buys 8-ounce, she pays $1.9 per ounce; when she buys 12-ounce, she pays $0.7 per ounce, and when she buys 16-ounce, she pays $0.14 per ounce.

Drawing the budget line

The budget constraint will be given by:

1.9x₁ + 0.7x₂ + 0.14x₃ = 5.75

Where $5.75 is Debra’s income, and x₁,x₂, andx₃ are the three consumption bundles.

The following figure shows Debra’s budget line.

The budget line has two kinks (at 8 & 12) showing different elasticities for different bundles.