Question

Suppose you are given the following equation for a budget constraint:

                                    Good Y = -6*Good X + 600

            Answer each question. Show your work.

            a) If the price per unit of Good Y is $2, what must be the price of Good X? (3 points)

            b) What is the maximum amount of Good X this consumer would be able to purchase?                           (2 points)

            c) If this consumer purchases 15 units of Good Y, what quantity of Good X could he/she                          purchase? Round any decimal to nearest whole number. (3 points)

Answer 1

a) Budget constraint is PX*GoodX + PY*GoodY = income
So, PY*GoodY = -PX*GoodX + income
We have, Good Y = -6*Good X + 600
When PY = 2; we get,
2*Good Y = 2*(-6*Good X + 600)
So, 2*Good Y = -12*Good X + 1200
Thus, price of good X is $12

b) Good Y = -6*Good X + 600
Maximum amount of good X is tha for which good Y = 0
Thus, 0 = -6*Good X + 600
So, 6*GoodX = 600
So, Good X = 600/6
Thus, good X = 100

c) Good Y = 15 = -6*Good X + 600
So, 6*GoodX = 600 - 15 = 585
So, Good X = 585/6 = 97.5
Thus, good X = 98