# Optimal choice on budget line

##### Intros
###### Lessons
1. Optimal Choice on Budget Line Overview:
2. Finding the Optimal Choice
• Maximize Utility on Budget Line
• Indifference Curve Intersects Budget Line
• Maximized when Budget Line is Tangent to IC
3. Changes to Price
• Decrease in price of a good
• Optimal choice is no longer the best
• Find a new indifference curve
• New optimal choice
4. Changes to Income
• Decrease in income
• Optimal choice is no longer the best
• Find a new indifference curve
• New optimal choice
##### Examples
###### Lessons
1. Finding & Predicting Optimal Choices
Suppose Vincy spent all her income on 3 pencils for $2 each and 2 erasers for$6 each. Now the price of pencils rises to $3 and the price of erasers decrease to$2.
1. Can Vincy still buy 3 pencils and 2 erasers?
2. What situation does Vincy prefer: pencils for $2 each and erasers for$6 each, or pencils for $3 each and erasers for$2 each?
2. Suppose Vincy spent all her income on 4 cups of tea for $3 each and 3 cups of coffee for$4 each. Now the price of tea decreases to $1.50 and the price of coffee increases to$8.
1. Can Vincy still buy 4 cups of tea and 3 cups of coffee?
2. What situation does Vincy prefer: cup of tea for $3 and cup of coffee for$4, or cup of tea for $1.50 and cup of coffee for$8.
3. Kevin's income is $16 a week. The price of a tea bag is$2 and the price of a slice of pizza is $4. The graph below shows Kevin's preference map for tea and chicken. 1. What quantities of tea bags and pizza will Kevin buy? 2. If the price of tea goes to$4 and everything else remains the same, then what quantities of tea bags and pizza will Kevin buy?
4. Kevin's income is $50 a week. The price of a chocolate is$5, and the price of vanilla is $10. The graph below shows Kevin's preference map for tea and chicken. 1. What quantities of chocolate and vanilla will Kevin buy? 2. If the price of vanilla goes to$25 and everything else remains the same, then what quantities of chocolate and vanilla will Kevin buy?
###### Topic Notes

Finding the Optimal Choice

The optimal choice from a combination of goods is attained when all income is spent, and the consumer is on the highest attainable indifference curve.

In other words, the optimal choice is attained when the budget line is tangent to the indifference curve.

Changes to Price

Recall that the budget line can be moved when there is a change in price of a good. When the budget line is moved, the optimal choice will also be changed.

We will look at 4 different cases in which the budget line changes, and how it affects the optimal choice.

Case 1: A decrease in the price of good x.

In this case, you can attain an indifference curve with higher utility, thus gaining a better optimal choice.

Case 2: An increase in the price of good x.

In this case, you attain an indifference curve with lower utility, thus attaining a lower optimal choice.

Case 3: A decrease in the price of good y.

In this case, you can attain an indifference curve with higher utility, thus gaining a better optimal choice.

Case 4: An increase in the price of good y.

In this case, you attain an indifference curve with lower utility, thus attaining a lower optimal choice.

Changes to Income

Recall that the budget line can be shifted when there is a change in income. Let’s look at two cases where the budget line shifts, and how it affects the optimal choice.

Case 1: A decrease in income.

In this case, you attain an indifference curve with lower utility, thus attaining a lower optimal choice.

Case 2: An increase in income.

In this case, you can attain an indifference curve with higher utility, thus gaining a better optimal choice.