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Consumer Theory and Budget Line

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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, …show more content…

Steps:
1. X+4Y=60
2. X=-4Y+60, if Y=0, then X=60
3. Y=-(0.25)X+15, if X=0, then Y=15
4. So the points (0, 15) and (60, 0) are on the curve
Thus, we can draw the diagram of budget line as follow:

So the opportunity set in this case is the shadow area shown above.
c. If the price of good X increases to $20, then the equation will change to 600=20X+40Y. So the new budget line is shown below:
Thus, the budget line will rotates clockwise as shown above. The opportunity set will decrease which means consumer has less options of quantity combination of goods.
d. Yes, it will alter the market rate of substitution. This is because the slope of budget line changes. Also, because the price of good X is increase, so we have to give up more amount of good Y in order to purchase a certain amount of good X. So the change in part c will alter the market rate of substitution in this

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