Final answer:
To demonstrate the budget constraint for José spending $56 on t-shirts and movies, plot the intercepts at (0, 8) for movies and (4, 0) for t-shirts on a graph, connect them to form the budget line, and understand the slope shows the trade-off between the goods.
Step-by-step explanation:
Creating a Budget Constraint Graph
The question involves creating a graph that reflects a budget constraint scenario, where the x-axis represents the number of t-shirts and the y-axis represents the total cost. To visualize the budget constraint for José, who has a fixed amount to spend, we plot the maximum number of t-shirts and movies he can afford on a graph. The slope of the budget constraint is calculated using the rise-over-run formula.
Firstly, we determine the vertical and horizontal intercepts from the given budget constraint. José has $56 to spend, the price of one T-shirt is $14, and the price of one movie is $7. Hence, the vertical intercept is at eight movies (total budget divided by the price of one movie: $56/$7=8), implying that if José spends all his money on movies, he can buy eight. The horizontal intercept is four t-shirts ($56/$14=4), showing that if he spends all on t-shirts, he can buy four.
Now, we plot these intercepts on a graph. The point (0, 8) represents zero t-shirts and eight movies, and the point (4, 0) represents four t-shirts and no movies. We draw a straight line connecting these two points. This line represents all possible combinations of t-shirts and movies José can purchase, given his budget constraint. The slope of this line is the change in the number of movies divided by the change in the number of t-shirts, which is -8/4, simplifying to -2. This slope reflects the trade-off between buying movies and t-shirts; for every t-shirt José decides to buy, he has to give up two movies.
The graph effectively illustrates the concept of scarcity and making choices under a budget constraint, as well as the trade-offs involved in decision-making. By plotting such a graph, we can explore how individuals allocate resources efficiently to maximize utility.