When the price of X is $1 and the price of Y is $1 and income is I, Joe Panther spends $100 on good X. One day Joe is walking down Downer street and is dismayed to discover that the price of good X has increased to $2. However, moments later Joe is delighted to find a $100 bill on the street. Use budget lines and indifference curves to answer the following question, leaving his unknown income as the variable I. Assume that he has normal convex shaped indifference curves and that he spends all of his income.
A)How many units of goods X and Y does Joe purchase before the price increase and finding the $100? Part of your answer will be in terms of prices and income.
B)After the price increase and finding the money can Joe still afford the same number of units of X and Y as in part A?
C)Is Joe better off, worse off, or just the same as before the price increase and finding the money? In other words, is utility higher in part A) or when Px=2 and income is I+100?
To answer these questions, we need to analyze Joe's budget lines and indifference curves.
A) Before the price increase and finding the $100 bill:
First, let's assume the price of good X is Px and the price of good Y is Py. According to the given information, when Px and Py are both $1 and Joe's income is I, he spends $100 on good X.
To determine the number of units of goods X and Y Joe purchases, we need to construct a budget line. The budget line represents the different combinations of goods X and Y that Joe can afford based on his income and the prices.
The equation for Joe's budget line is: Px * X + Py * Y = I. Since Joe spends all of his income, the equation becomes: Px * X + Py * Y = $100.
Let's assume Joe purchases X units of good X and Y units of good Y. By substituting these variables into the budget line equation, we get: $1 * X + $1 * Y = $100, which simplifies to X + Y = 100.
Since we don't have any specific values for X and Y, we can express the answer in terms of X and Y units.
B) After the price increase and finding the $100 bill:
Now, let's consider what happens when the price of good X increases to $2 and Joe finds a $100 bill on the street. At this point, Joe's income is I + $100.
We need to determine if Joe can still afford the same number of units of X and Y as before the price increase and finding the money. This can be done by constructing a new budget line.
The new budget line equation becomes: $2 * X + Py * Y = I + $100. Since we know that X + Y = 100, we can substitute this into the equation: $2 * (100 - Y) + Py * Y = I + $100. Simplifying this equation will give us the relationship between X units and Y units.
C) Utility comparison:
To determine if Joe is better off, worse off, or just the same, we need to consider his utility. The utility is determined by the indifference curves.
The given information states that Joe has normal convex-shaped indifference curves. This means that Joe prefers a combination of goods that includes both X and Y. Higher indifference curves represent higher utility levels.
To compare the utility before and after the price increase and finding the money, we need to determine the respective utility levels using the indifference curves. The utility level with the highest indifference curve represents a higher level of utility.
By comparing the utility levels in both scenarios, we can determine if Joe is better off, worse off, or just the same.
Please note that without specific numerical values for income, prices, or the shape and location of indifference curves, we can only explain the general methodology to answer these questions.