Chapter 4: Consumer Behavior/Budget Line
1) A consumer has $400 (budget) to spend on goods X and Y. The market prices of these two goods are Px=$20 and Py=$50
- a) What is the market rate of substitution (slope of budget line) between good X and good Y
- b) Illustrate/write the consumer’s budget line in a carefully labeled diagram
- c) On the same diagram, show how the consumer’s budget line changes if income increases to $600
- d) If the price of good X increases to $40 and income (budget) is $400, how the does the budget line change? Show it on separate diagram identifying the old and new budget line.
- e) Write the regression equation of for the consumer’s budget line (Y) after price increase.
Answer:
- a) MRS=-PX/PY=-20/50=-0.4 (slope of budget line)
- b) Find max of Good X=M/Px=400/20=20
Good Y max=M/Py=400/50=8
Good X max= x axis (20)
Good Y max= y axis (8)
- c) Right shift of the budget line with new income/budget (600 dollars)
Find Good X max=600/20=30
Find Good Y max=600/50= 12
Good X max= x axis (30)
Good Y max= y axis (12)
- d) Remember the rule: Price increase in good X rotates the budget line clock wise; price decrease in good X rotates it counter-clockwise (refer to course slides).
Max Good X changes due to price increase
Good X max= M/Px= 400/40=10
- e) Remember the rule: Regression equation of the budget line is:
Y=(M/Py)-(Px/Py)X
Therefore, Y after price increase=Y=(M/Py)-(Px/Py)X
New price of X is 40
y= (400/50)-(40/50)X
y=8-0.8X
Remember the rules: Change income versus Change in Price
Another example: Figure below illustrates an increase in the price of good X from $5 to $10. See how the budget line rotates clockwise (Note that X and Y are maximum amount consumed). With an increase in the price of Good X (relative to Y) leads to less consumption of good X. Max consumption drops from 50 units of good X to 25 units of good X.
2) End of Chapter 4 textbook: Consumer has $400 (budget) to spend on goods X and Y. The market prices of these two goods are Px=$10 and Py=$40
- a) What is the market rate of substitution (slope of budget line) between good X and good Y
- b) Illustrate/write the consumer’s budget line in a carefully labeled diagram
- c) On the same diagram, explain how the consumer’s budget line changes if income increases by $400. How does the $400 increase in income alter the market rate of substitution between good X and good Y?
- The market rate of substitution is .
- See Figure 4-1.
Remember the rule: Regression equation of the budget line is:
Y=(M/Py)-(Px/Py)X
Y=(400/40)-(10/40)X
Y=10-2.5X
- Increasing income to $800 (income increases by $400) expands the budget set, as shown in Figure. Budget line shifts to the right. However, since the slope is unchanged, so is the market rate of substitution.