The figure below shows a consumer maximizing utility at two different prices (the left panel)and the consumer's demand for good X at the same two prices of good X (the right panel).The price of good Y is $4.50.What is the consumer's income?
A)$250
B)$280
C)$320
D)$360
E)$400

Question

The figure below shows a consumer maximizing utility at two different prices (the left panel)and the consumer's demand for good X at the same two prices of good X (the right panel).The price of good Y is $4.50.What is the consumer's income? 
A)$250 
B)$280 
C)$320 
D)$360 
E)$400

Quizplus · Accepted Answer

In the right panel, we can see that the consumer purchases 10 units of X when the price is $8 and 12 units when the price is $6. At the higher price, the consumer spends 10 x $8 = $80 on good X, and at the lower price, the consumer spends 12 x $6 = $72 on good X. The difference in spending on good X, $80 - $72 = $8, is equal to the amount the consumer spends on good Y. Therefore, the consumer's income is $8 + (10 x $4.50) = $53 at the higher price, and $8 + (12 x $4.50) = $62 at the lower price. Since the consumer spends more at the lower price, we use the lower income, which is $62, to solve for the budget line equation: 
$62 = 10X + $4.50Y 
Solving for Y when X = 0, we find that the intercept of the budget line is $62/ $4.50 = $13.78 (rounded to two decimal places). Therefore, the consumer's income is $13.78 x 20 (the quantity of Y demanded when the price is $4.50) = $275.60. However, we must also account for the $8 spent on good Y. Therefore, the final answer is $275.60 + $8 = $283.60, which is closest to option D, $360.

The Figure Below Shows a Consumer Maximizing Utility at Two