question archive Suppose a consumer purchases two goods, food, and clothing
Suppose a consumer purchases two goods, food, and clothing
Subject:EconomicsPrice: Bought3
Suppose a consumer purchases two goods, food, and clothing. He has the utility function U(x, y) = xy. Now suppose that he has an income of $144 per week and that the price of clothing is Py = $2 per unit. Suppose that the price of food is initially Pay = $8 per unit and that the price subsequently falls to Pxz = $2 per unit.
Step 1: Find the initial consumption basket A when the price of food is $8.
The budget line when the price of food is $8 is ___x+___y=___. The slope of the budget line is ___. The slope of the indifference curve is -y/x. When the budget line is tangent to the indifference curve, at that basket y=___x. When the price of x is $8, the consumer buys ___ units of x and ___ units of y.
Step 2: Find the final consumption basket C when the price of food is $2.
The budget line when the price of food is $2 is ___x+___y=___. The slope of the budget line is ___. The slope of the indifference curve is -y/x. When the budget line is tangent to the indifference curve, at the basket y = (___)x. When the price of x is $2, the consumer buys ___ units of x.
Step 3: Find the decomposition basket to find the substitution effect and the income effect
The decomposition basket must satisfy two conditions. First, it must lie on the original indifference curve along with basket A. Recall that this consumer's utility function is , so at basket A, utility _____. At basket B the amounts of food and clothing must also satisfy xy = ____. Second, the decomposition basket must be at the point where the decomposition budget line is tangent to the indifference curve. Remember that the price of food on the decomposition budget line is the final price of $____. The tangency occurs when , that is when y = (___)x. When we solve the two equations xy = ___ and y = ___x, we find that, at the decomposition basket, x = ___ units of food. Here, due to the decrease in the price of x, the substitution effect, which ensures that the consumer gets the initial level of satisfaction, is ___ - ___ = ___ units of x. However, the consumer then notices that she still has some money left, and spending the excess amount, she can move to a higher indifference curve. She will do so by adding ____ units of x which is the income effect.
The decomposition basket must satisfy two conditions. First, it must lie on the original indifference curve U1 along with basket A. Recall that this consumer's utility function is U{x, y) = xy, so at basket A, utility U{x, y] = xy = . At basket B the amounts of food and clothing must also satisfy kg = _. Second, the decomposition basket must be at the point where the decomposition budget line is tangent to the indifference curve. Remember that the price of food P1. on the decomposition budget line is the final price of 5 . The tangencyr occurs when "—3: = %, that is when yr = | In. When we solve the two equations Jig M :- 1' = _ and 1; = _x, we ?nd that, at the decomposition basket, I = _ units of food. Here, due to the decrease in the price of x, the substitution effect, whid": ensures that the consumer gets the initial level of satisfaction, is _ - _ = _ units of it. However, the consumer then notices that she still has some money,r left, and spending the excess amount, she can move to a higher indifference cu rue. She will do so by adding units of k which is the income effect.
