Consumer Theory and Budget Line
Week 6 Chapter 4: The theory of Individual Behavior
Question 1. Page 154 ( with some modifications) A consumer has $300 to spend on goods X and Y. The market prices of these two goods are Px = $15 and Py = $5.
a. Draw the budget constraint. i.e provide a carefully labeled diagram
b. What is the market rate of substitution? Give an interpretation.
c. Illustrate the consumer’s opportunity set in part a) above.
d. Show how the consumer’s opportunity set changes if income increases by $300.
e. Does the increase of income by $300 in part d) above alter the market rate of substitution between goods X and Y?
Answer:
a. The total budget is $300. Px and Py are used to stand for market prices of two goods x and y. Hence, 300=15X+5Y. Now if the entire budget money is spent on good X, then Y=0, X=20. Also, if the entire budget money is spent on good Y, then X=0, Y=60. So the maximum amount of good X is 20 and the maximum amount of good Y is 60.
Steps:
1. 300=15X+5Y
2. Y=-3X+60, if X=0, then Y=60
3. X=-(1/3)Y+20, if Y=0, then X=20
4. So Points (0, 60) and (20, 0) are on the curve
Therefore, The budget constraint diagram can be drawn and is shown as follow:
b. The market rate of substitution is the rate at which good X (or good Y) may be traded for good Y (or good X) in the market. It is the slope of the budget line. So if we calculate the slope of the budget line above, we can get the market rate of substitution in this case.
Steps:
1. The Slope of budget line= (M/Py)/(M/Px)= Px/Py
2. Px/Py=15/5=3
3. Thus, the market rate of substitution in this case is 3.
Interpretation: This means that in order to get one unit of good X, we have to give up three units of good Y. This reflects the meaning of substitution.
c. The opportunity set (also called the budget set) is th bundles of goods a consumer can afford. This means that in this case consumer can buy different quantity combinations of good X and good Y within the limit of $300. So in the diagram
Question 1. Page 154 ( with some modifications) A consumer has $300 to spend on goods X and Y. The market prices of these two goods are Px = $15 and Py = $5.
a. Draw the budget constraint. i.e provide a carefully labeled diagram
b. What is the market rate of substitution? Give an interpretation.
c. Illustrate the consumer’s opportunity set in part a) above.
d. Show how the consumer’s opportunity set changes if income increases by $300.
e. Does the increase of income by $300 in part d) above alter the market rate of substitution between goods X and Y?
Answer:
a. The total budget is $300. Px and Py are used to stand for market prices of two goods x and y. Hence, 300=15X+5Y. Now if the entire budget money is spent on good X, then Y=0, X=20. Also, if the entire budget money is spent on good Y, then X=0, Y=60. So the maximum amount of good X is 20 and the maximum amount of good Y is 60.
Steps:
1. 300=15X+5Y
2. Y=-3X+60, if X=0, then Y=60
3. X=-(1/3)Y+20, if Y=0, then X=20
4. So Points (0, 60) and (20, 0) are on the curve
Therefore, The budget constraint diagram can be drawn and is shown as follow:
b. The market rate of substitution is the rate at which good X (or good Y) may be traded for good Y (or good X) in the market. It is the slope of the budget line. So if we calculate the slope of the budget line above, we can get the market rate of substitution in this case.
Steps:
1. The Slope of budget line= (M/Py)/(M/Px)= Px/Py
2. Px/Py=15/5=3
3. Thus, the market rate of substitution in this case is 3.
Interpretation: This means that in order to get one unit of good X, we have to give up three units of good Y. This reflects the meaning of substitution.
c. The opportunity set (also called the budget set) is th bundles of goods a consumer can afford. This means that in this case consumer can buy different quantity combinations of good X and good Y within the limit of $300. So in the diagram