Question

Peter consumers sandwiches (good 1, with price p1) and juice (good 2, with price p2). His demand function for sandwiches is x1* = 2m / 3p1 where m is his income.

(a) Use the budget constraint to find Peter's demand for juice.
(b) Suppose m = $270, p1 = $5 and p2 = $2. Find Peter's optimal consumption bundle and call it A.

Answer 1

To find Peter's demand for juice, use the budget constraint equation and Peter's demand function for sandwiches. Plug in the given values for income and prices to find the optimal consumption bundle.

Step-by-step explanation:

To find Peter's demand for juice, we need to use the budget constraint. The budget constraint equation is given by:

Budget = p1 * x1 + p2 * x2

In this case, Peter's budget is his income, m, which is $270. Given that p1 is $5 and p2 is $2, we can substitute these values into the equation to get:

$270 = $5 * x1 + $2 * x2

Now we need to find Peter's demand for juice, x2. We can do this by rearranging the equation:

x2 = (m - p1 * x1) / p2

Substituting the values we know:

x2 = ($270 - $5 * x1) / $2

From here, we can substitute Peter's demand function for sandwiches into the equation:

x2 = ($270 - $5 * (2m / 3p1)) / $2

Simplifying, we get:

x2 = ($270 - $10m / 3) / $2

This gives us Peter's demand for juice as a function of his income and the prices of sandwiches and juice.