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

For normal goods, the ICC slope is positive, meaning that as income increases, the quantity demanded of the good also increases. The ICC slope can be calculated using the formula: ICC slope = (Price of good on y-axis / Price of good on x-axis) * (-dU/dx). In this case, the price of games is on the y-axis and the price of toy airplanes is on the x-axis. Plugging in the given utility function, we get the following partial derivatives: dU/dg = 0.6g^-0.4a^0.6 and dU/da = 0.4g^0.6a^-0.6. Therefore, the ICC slope for games is (20/10) * (-0.6/(0.4g^0.6a^-0.6)) = -3g^0.6/a^-0.6 and the ICC slope for toy airplanes is (10/20) * (-0.4/(0.6g^-0.4a^0.6)) = -0.333g^-0.4a^0.6. When income increases from $100 to $200, both ICC slopes become less negative, indicating that both games and toy airplanes are normal goods. The ICC slopes can be calculated at the two income levels and compared to confirm this.

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