Question

Ben allocates his lunch budget between two goods, pizza and burritos. a. Illustrate Ben's optimal bundle on a graph with pizza on the horizontal axis. b. Suppose now that pizza is taxed, causing the price to increase by 20 percent. Illustrate Ben's new optimal bundle. c. Suppose instead that pizza is rationed at a quantity less than Ben's desired quantity. Illustrate Ben's new optimal bundle.

Short answer

When prices increase or goods are rationed, a consumer's optimal bundle changes. The consumer will typically buy less of a good whose price has increased and, in the case of rationing, will buy up to the rationed quantity, adjusting other purchases to maximize utility given the budget constraint.

Step-by-step solution

Illustrate the Initial Optimal Bundle

Draw two axes on a graph, with pizza represented on the horizontal axis and burritos represented on the vertical axis. Ben's original optimal bundle is where his budget line, determined by the prices of pizza and burritos and his income, touches his highest attainable indifference curve which shows his preferences between the two goods. Label this point A and indicate the quantity of pizza and burritos.

Effect of Increase in Price of Pizza

A 20% increase in the price of pizza will change the slope of the budget line, making it steeper. This means that Ben will have to give up more burritos to obtain each additional pizza, so he will probably buy fewer pizzas and more burritos. Draw the new budget line and Ben's new optimal bundle where this budget line is tangent to his highest attainable indifference curve. Label this point B and indicate the new quantities.

Effect of Rationing of Pizza

Rationing means there's a limit on the quantity of pizza Ben can purchase. This constraint is represented by a vertical line at the rationed quantity of pizza. Ben's new optimal bundle is where this line intersects with his highest attainable indifference curve within the new budget constraint. Draw this vertical line and the new optimal bundle and label this point C. Indicate the rationed quantity of pizza and the new quantity of burritos.