Question

If Melle Mel (AKA Grandmaster Melle Mel of Grandmaster Flash and the Furious Five) has a choice of purchasing good Y on the y-axis and good x on the x-axis. He has a budget of $500. The price of good Y is $5 or Py = $5. His x-intercept is 50, or the maximum amount of good X he can buy is 50. What is the price of good x or Px and the slope of his budget line? Hint: Px*X + Py*Y = I, where I is income or budget.

Answer 1

The price of good X (Px) is $10, and the slope of the budget line is -2. The budget constraint is represented by the equation $10*X + $5*Y = $500, with the trade-off between goods X and Y illustrated by the slope.

Step-by-step explanation:

If Melle Mel has a budget of $500 to purchase good Y and good X, and the price of good Y is $5 (Py = $5), we need to find the price of good X (Px) and the slope of his budget line. According to his x-intercept, the maximum amount of good X he can buy is 50.

Therefore, if he spends all his budget on good X, it would cost him $500, so the price of good X is found by dividing the total budget by the quantity of good X, which gives us Px = $500 / 50 = $10. The budget line equation is Px*X + Py*Y = I, which translates here to $10*X + $5*Y = $500.

The slope of the budget line is determined by the negative ratio of the prices of the two goods. Thus, the slope is -Px/Py, which in this case, is -($10/$5), giving us a slope of -2. Hence, for every unit decrease in good Y you can afford two extra units of good X, given the budget constraint.