A consumer\'s budget set for two goods and (X and Y) is 500 2X + 4Y. Illustrate

Question

A consumer's budget set for two goods and (X and Y) is 500 2X + 4Y. Illustrate the budget set in a diagram. Does the budget set change if the prices of both goods double and the consumer's income also doubles? Explain. Given the equation for the budget set, can you determine the prices of the two goods? The consumer's income? Explain

Explanation / Answer

2x + 4y = 500 --> maximum budget Px = 2 Py = 4 When you buy all x with $500, x = 500/2 = 250 you can buy 250 x When you buy all y with $500, y = 500/4 = 125 you can buy 125 y So with x on the X axis, y on the Y axis, the graph will be a straight line equation, x-axis intercept = 250 y-axis intercept = 125 b. when price doubles, and budget doubles, the budget set will not change. our new budget equation will be: 4x + 8 y = 1000 and you can see that when you buy all x, you can only afford 250 x, and when you buy all y, you can only afford 125y, exactly the situation you're in when prices and budget are half as much. This is because both prices and budget increases at the same pace, therefore there is no real change to the consumption set that you can have. c.Price of X = 2 Price of Y = 4 Income = 500 For budget eqn, --> aX + bY = M where a = Px b = Py M = budget

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