Question

A common marketing tactic among many liquor stores is to offer their clientele quantity (or volume) discounts. For instance, the second-leading brand of wine exported from Chile sells in the United States for$\backslash (15$ per bottle if the consumer purchases up to eight bottles. The price of each additional bottle is only$\backslash )8$ . If a consumer has $\backslash (200$to divide between purchasing this brand of wine and other goods, graphically illustrate how this marketing tactic affects the consumer’s budget set if the price of other goods is$\backslash )1$ . Will a consumer ever purchase exactly eight bottles of wine? Explain.

Short answer

A consumer can never buy exactly eight bottles of wine because as illustrated on the graph, the price of the wine is lesser after the curve and the best time to purchase is when the budget set is flat.

Step-by-step solution

Finding the budget line

Use the following equation,

$P_{x}X+P_{y}Y=M$

Here,

M is the Consumer’s income

$P_x$is the Price of the wine per bottle

$P_y$is the price of all other goods.

Given,

The price of wine per bottle is$\$15$

And consumer’s income is$\$200$

The budget line will be,

$$\begin{gathered} P_{x}X+P_{y}Y=M \\ 15X+P_{y}Y=200 \end{gathered}$$

When, the price of wine per bottle is$\$8$

The budget line will be,

$$\begin{gathered} P_{x}X+P_{y}Y=M \\ 8X+P_{y}Y=200 \end{gathered}$$

Plotting the graph

As seen in the graph, there is a sharp curve uptil Point, where consumer consumesunits of all other goods andunits of wine. Because of the decrease in price, the slope changes to. Along the decrease in the price is the increase in the consumers income which results into a flat budget set.

Therefore, a consumer can never buy exactly bottles of wine because based on the graph, the price of the wine is lesser after the curve and the best time to purchase is when the budget set is flat.