An individual derives utility from games,g (y-axis),and toy airplanes,a (x-axis),described by the utility function U(g,a)= g^0.6a^0.4.The price per game is $20 and the price of toy airplanes is $10.Using the slope of the income consumption curve (ICC),determine whether games and toy airplanes are normal or inferior goods when income increases from $100 to $200. A) Both goods are normal goods with an ICC slope of . B) Both goods are normal goods with an ICC slope of . C) Both goods are inferior goods with an ICC slope of - . D) Both goods are inferior goods with an ICC slope of - .

Question

Quizplus · Accepted Answer

To determine whether a good is normal or inferior, we need to look at the sign of the slope of the income consumption curve (ICC). If the slope is positive, then the good is a normal good; if it is negative, then the good is an inferior good.

The ICC can be derived by holding one good's consumption constant and varying the other good's consumption as income increases. Since we have a utility function, we can use it to derive the demand functions for each good, which will allow us to calculate the bundles of goods that the individual will consume at different income levels.

The demand functions for games and toy airplanes are:

g = 20*(2*a/3)^(-5/3)
a = 10*(3*g/4)^(-5/3)

Using these demand functions, we can calculate the bundles of goods that the individual will consume at two different income levels: $100 and $200.

At an income of $100, the individual's budget constraint is:

20g + 10a = 100

Plugging in the demand function for a, we get:

20g + 10*(10*(3*g/4)^(-5/3)) = 100

Simplifying and solving for g, we get:

g = 1.807

Plugging this back into the demand function for a, we get:

a = 7.467

So the individual will consume 1.807 games and 7.467 toy airplanes at an income of $100.

Similarly, at an income of $200, the individual's budget constraint is:

20g + 10a = 200

Plugging in the demand function for a, we get:

20g + 10*(10*(3*g/4)^(-5/3)) = 200

Simplifying and solving for g, we get:

g = 3.051

Plugging this back into the demand function for a, we get:

a = 5.491

So the individual will consume 3.051 games and 5.491 toy airplanes at an income of $200.

We can use these bundles to calculate the slope of the ICC by taking the difference in toy airplane consumption divided by the difference in income:

ICC slope = (a2 - a1)/(y2 - y1) = (5.491 - 7.467)/(200 - 100) = -1.988

Since the ICC slope is negative, both games and toy airplanes are inferior goods. Therefore, the only answer choice that reflects this is A: Both goods are normal goods with an ICC slope of 11ea66c3_5709_3bc3_a97f_ff9840a92183_TB6808_11. The other answer choices incorrectly state that both goods are normal goods.

An Individual Derives Utility from Games,g (Y-Axis),and Toy Airplanes,a (X-Axis),described