Suppose a consumer has an income of $800 per month and that she spends her entire income each month on beer and bratwurst. The price of a pint of beer is $5, and the price of a bratwurst is $4. Which of the following combinations of beers and bratwursts represents a point that would lie directly on the consumer's budget constraint?
A)160 beers and 200 bratwursts
B)40 beers and 50 bratwursts
C)80 beers and 100 bratwursts
D)80 beers and 0 bratwursts

Question

Quizplus · Accepted Answer

The consumer's monthly income is $800 per month.

Let P be the price of beer, which is $5 per pint.
Let Q be the price of bratwurst, which is $4 per bratwurst.
Let B be the number of beers she purchases per month.
Let W be the number of bratwursts she purchases per month.

Her budget constraint can be expressed as:

P × B + Q × W = Income

Substituting in the values of P, Q, and Income, we get:
5B + 4W = 800

This is a linear equation in two variables, B and W. We can draw the budget line by solving for W in terms of B:

4W = 800 - 5B
W = 200 - 1.25B

This equation describes a straight line with a slope of -1.25 and an intercept of 200 on the vertical axis.

Now, we can check which of the given options lie on this budget line by substituting the values of B and W:

A) 160 beers and 200 bratwursts
4(200) + 5(160) = 1500, which is greater than her income of $800. This option is not feasible.

B) 40 beers and 50 bratwursts
4(50) + 5(40) = 380, which is less than her income of $800. This option is feasible, but not the best choice.

C) 80 beers and 100 bratwursts
4(100) + 5(80) = 800, which is exactly equal to her income of $800. This option lies on the budget line and is therefore the best choice.

D) 80 beers and 0 bratwursts
4(0) + 5(80) = 400, which is less than her income of $800. This option is feasible, but not the best choice.

Suppose a Consumer Has an Income of $800 Per Month