Question

note: please hand write your answers on a sheet of paper and upload them to canvas. you may scan them or take a picture. please make sure your writing is legible/readable and your images are clear. alternatively, you may also type your answers however many of the questions require you to use illustrations to make your points. jpg or pdf file format only!
suppose larry legend has a budget of $360 and is deciding between purchasing membership to hulu which costs $60 and netflix which costs $10.

1. graph the line that demonstrates your example. be sure to label the y - axis, x - axis, line, and how to identify the opportunity cost in the graph. (please draw by hand and attach your graph by taking a picture of it.)
2. calculate the opp cost.
3. show what will happen graphically if larry legends budget decreases to $240.
4. explain how the opportunity cost changes in your graph.

Explanation:

Step1: Define variables

Let $x$ be the number of Hulu memberships and $y$ be the number of Netflix memberships. The budget constraint equation for the initial budget of $B_1 = 360$ is $60x + 10y=360$, which can be rewritten as $y = 36 - 6x$. For the new budget $B_2=240$, the equation is $60x + 10y = 240$, or $y=24 - 6x$.

Step2: Calculate opportunity - cost

The opportunity - cost of one Hulu membership in terms of Netflix memberships is the absolute value of the slope of the budget - line. For the budget line $y = a - bx$, the slope is $-b$. Here, the slope of both budget lines is $-6$. So the opportunity cost of one Hulu membership is 6 Netflix memberships. This is because for every additional Hulu membership purchased, 6 Netflix memberships must be given up due to the price ratio ($\frac{60}{10}=6$).

Step3: Analyze graphical change

When the budget decreases from $360$ to $240$, the budget - line shifts inwards parallelly. The $y$ - intercept decreases from 36 to 24, and the $x$ - intercept decreases from $\frac{360}{60}=6$ to $\frac{240}{60} = 4$. The slope remains the same ($-6$), so the opportunity cost remains constant.

Answer:

The opportunity cost of a Hulu membership is 6 Netflix memberships. When the budget decreases from $360$ to $240$, the budget - line shifts inwards parallelly, and the opportunity cost remains unchanged at 6 Netflix memberships per Hulu membership.