Suppose a consumer has a daily income of $48 and purchases just two goods, A and B.  The price of A is $8 and the price of B is $6.In a graph, draw the budget line for the consumer.  Indicate...

Suppose a consumer has a daily income of $48 and purchases just two goods, A and B.  The price of A is $8 and the price of B is $6.

In a graph, draw the budget line for the consumer.  Indicate the area of the graph that is attainable given the income and the area that is unattainable.

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txmedteach's profile pic

Posted on

This question looks complex, but it is actually a small set of easy steps. Let me show you:

First, let's figure out what a budget line is (By the way, I've always heard it as budget constraint, see link below). All this line shows is that given the income level you've provided, how many ways can the consumer combine purchases of Good A and Good B such that he stays below his daily income? More mathematically, you see it expressed:

`Ax + By <= I`

Where `A` is the cost of Good A, `B` is the cost of Good B, `x` is the number of units of Good A, `y` is the number of units of Good B, and `I` is the consumer's income.

In other words the consumer is not allowed to overspend!

So, how do we construct this line? Well, let's start with the values we know:
`A= $8`

`B = $6`

`I = $48`

So, our equation has become:

`8x+6y <= 48`

Now, just remember that on our axes with this x and y, the x-axis represents the number of good A purchased, and the y-axis represents the number of good B purchased.

To make the budget line, you can simply find the x and y intercepts of the line and just draw the line between them. This is the same thing as the consumer buying all that he can of Good A or Good B. To find the intercepts, you recognize that at the y-intercept, x =0, and at the x-intercept, y = 0. Let's calculate these now:

Y-intercept (x=0) (only Good B purchased):

`8(0)+6y <= 48`


Divide both sides by 6:

`y <= 8`

So, our y-intercept is (0,8).

Now to the x-intercept (y=0) (Only Good A purchased):



Now, divide both sides by 8:

`x <=6`

So our x-intercept is (6,0). We are ready to draw our graph. Let's first plot the intercepts:

Now, we can simply draw the line in between them. Notice that we will draw a solid line (indicating points on the line are in our budget constraint) because the equation we're using has a "less than or equal to" sign:

However, we're not done yet! We have just drawn this equation:

`8x+6y = 48`

But, our equation was `8x+6y<=48`! And intuitively, you can think of the extreme case that the consumer decides to by nothing, which would be represented by the point (0,0). Because this case makes sense, you know that every point between the axes and underneath the budget line is a plausible solution. This gives us our final solution (shaded in green):

Now, realize that you can't buy less than 0 of a given product. The green lines below the x-axis and to the left of the y-axis are just artifacts of the graphing program (ignore those parts).

Clearly, the area, then, that is unattainable is everything not inside that little triangle. For example, if the guy makes $48 /day, he certainly go out and buy 800 units of Good A and 5,000,000,000 units of Good B! so the area that is unattainable is anything above or to the right of the red line or its intercepts. Also, of course, anything with a negative coordinate is also necessarily unattainable (unless the consumer can sell merchandise...but this is why most stores require a receipt!).

Hope that helps!



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