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ECON 201 Lecture Notes - Lecture 2: Budget Constraint, Composite Good, Opportunity Cost

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School
Simon Fraser University
Department
Economics
Course
ECON 201
Professor
Alex Karaivanov

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Document Summary

We will consider two goods, 1 and 2. X1 how much the consumer is choosing to consume of good 1. M the amount of money the consumer has to spend or income. Therefore, the affordable consumption bundles and budget constraint can be shown by the following formula: p1x1 + p2x2 m. Budget set set of affordable consumption bundles at prices (p1, p2) and income m. The two-good assumption can be used to interpret one of the goods (x2) as representing everything else the consumer might want to consume. Good 2 $ the consumer can use to spend on other goods. P2 , since that"s the price of one dollar. Therefore, the budget constraint takes the form: p1x1 + x1 m. Therefore, good 2 composite good represents everything else a consumer might want to consume other than a specific good, or good 1. Budget line set of bundles that cost exactly m: p1x1 + p2x2 = m.

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Related Questions

Suppose that there are two goods (X and Y). The price of X is $2 per unitu, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8Y^.2

Consumer A has an income of $100, and Consumer B has an income of $300.

1. Derive the marginal utlities of goods X and Y for consumer A


2. Derive the marginal utilities of goods X and Y for consumer B


3. Set consumer A's MRS equal to the price ratio. Then use the budget constraint to solve for her optimal bundle


4. Set consumer B's MRS equal to the price ratio. Then use the budget contraint to solve for his optimal consumption bundle.


5. Calculate the MRS for each consumer at their optimal consumption bundles.


6. Suppose that there is another conusmer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's MRS at her optimal consumption bundle? Why?


Currently, the price of consuming housing x1 is lowered by the fact that home mortgage interest is tax deductible. Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from (p1-s) to p1. At the same time, the government lowers the tax on other consumption x2, lowering the price from (p2 + t) to p2.

a) Write down your original budget constraint assuming the consumer has income I.

b) Suppose the utility function u(x1, x2) = (1/3) lnx1 +lnx2 captures your tastes, and suppose I = 10, 000,

p1 = 10, p2 = 1, s = 6, and t = 1. Write out the utility maximization problem for this consumer

prior to any policy change.
c) How much housing and other goods will this consumer consume prior to any policy change? (show process)

d) When the policy change goes into effect, will this consumer still be able to afford the bundle you derived in (c)?

e) When the policy change goes into effect, what bundle will the consumer consume?

Assume that an individual consumes two goods, X and Y. The total utility (assumed measurable) of each good is independent of the consumption rate of other goods.
The price of X and Y are respectively $40 and $60. Use the following table of total utilities to answer the following questions.

Good Total utility X Total utility Y
 1  20  45
 2  38  78
 3  54  108
 4  68  135
 5  80  159
 6  90  180


a. The marginal utility of the fourth unit of Y is__________.
b. The marginal utility of the fifth unit of X is___________.
c. The marginal utility per dollar spent on the third unit of X is__________.
d. The marginal utility per dollar spent on the second unit of Y is__________.
e. If the consumer has $420 to spend, ______ unit of X and _______units of Y maximize utility subject to the budget constraint. Explain.
f. If the consumer has $220 to spend, _______ units of X and_______ units of Y maximize utility subject to the budget constraint. Explain.
g. If the consumer wanted 4 units of X and 6 units of Y, what would have to be his/her budget constraint in order to maximize his/her utility? Explain.