Your budget is such that if you spend your entire income of 20, you can afford...

Your budget is such that if you spend your entire income of 20, you can afford “bundle A”: (4 units of good x and 6 units of good y) or “bundle B”: (12 units of x and 2 units of y)

Specifically mark these two consumption bundles using the horizontal axis for good x. Draw the budget line in the graph and label all points and axes.

The slope of the budget line is called the marginal rate of technical substitution, MRT = -Px / Py = -Δy / Δx. Using the information in part a, what is the ratio of the price x to the price of y?
If you spent all your income on x, how much x could you buy? ____________________. If you spent all of your income on y how much y could you buy ______________________
What is the equation for the budget line?

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Solutions

Expert Solution

a) Shown in the image below where good x is on the horizontal axis and good y is on the vertical axis.

b) The slope of the budget line = -price of good x / price of good y = - change in good y / change in good x

In the question above, from bundle A to bundle B , the change in good y = 6 - 2 = 4

and, the change in good x = 12 - 4 = 8

So, the ratio of price of good x to price of good y = -4 / 8 = -1/2

which means that the price of good x is 1 and price of good y is 2.

c) The two bundles now considered here are (x, 0) and (12x, 2y) since the consumer is now spending his entire income on good x.So here change in good y is 2 i.e. 2 - 0 = 2

change in good x / change in good y = 1/2

Using bundle B, change in x = 2 X change in y

change in x = 2 X 2 = 4

So, if the consumer consumes only good x, then can consume 16 units of good x, i.e 12 + change in x = 12 + 4 = 16

The two bundles now considered here are (0, y) and (4x, 6y) since the consumer is now spending his entire income on good y. So, here change in good x is 4 i.e. 4-0 = 4.

change in good x / change in good y = 1/2

change in y = change in x / 2

change in y = 4/2 = 2

So, if the consumer consumes only good y, then he will consume 8 units of good y i.e. 6 + change in y = 6 + 2= 8

d) The equation of the budget line

(price of x X quantity of good x) + (price of good y X quantity of good y) = Income

(1 X x) + (2 X y) = 16 (In th above question income is given wrong, it should be 16 and not 20)

x + 2y = 16 is the answer.

Rahul Sunny answered 1 year ago

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