2. John likes coffee and cookies. The price for one cup of coffee is $1; the price for one cookie is $1. His marginal utility for coffee is 10 - x, where x is the amount of coffee. His marginal utility for cookies is 21 - 2 y, where y is the number of cookies. How many cups of coffee and units of cookies will John buy if he has only $10

3 cups of Coffee and 7 units of cookies

Explanation:

In order to maximize his utility John will satisfy the following relationship

The Rational Spending Rule for two goods, X and Y:

MUX/PX = MUY/PY

10 - x = 21 - 2y

10 - 21 + 2y = x

x = 2y - 11 ... equation (1)

A budget line shows combinations of two goods a consumer is able to consume, given a budget constraint. Here John's constraint is $10,

we have, cups of coffee (x) + units of cookies (y) = $10

x + y = 10

We substitute X with the value of x in equation (1)

(2y - 11) + y = 10

2y + y = 10 + 11

3y = 21

y = 7.

y is the number of cookies, therefore y = 7 units

x = 2y - 11 = 2 * 7 - 11 = 14 - 11 = 3

x is the amount of coffee, therefore x = 3 cups.

If John has $10 he will 3 cups of Coffee and 7 units of cookies