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Attendance trivia question:
The name of what company is formed from a portmanteau of Danish words that translate to English as "play well"?
Christopher Makler
Stanford University Department of Economics
Econ 50: Lecture 10
Resources
Technology
Stuff
Happiness
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Resources
Firms
Stuff
Consumers
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Resource
Owners
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Resources
Firms
Stuff
Consumers
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Resource
Owners
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Firms pay wages for labor
Firms pay rent on capital
Consumers pay prices for goods
Demand
Supply
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Suppose each good has a constant price
(so every unit of the good costs the same)
Suppose you have a given income \(m\)
to spend on goods 1 and 2.
Then bundle \(X = (x_1,x_2)\) is affordable if
Example: suppose you have \(m = \$240\) to spend on two goods.
Good 1 costs \(p_1 = \$3\) per unit.
Good 2 costs \(p_2 = \$4\) per unit.
Is the bundle (10,40) affordable (in your budget set)? What about the bundle (40,40)?
Draw your budget set.
How would it change if the price of good 1 rose to \(p_1' = \$6\) per unit?
How would it change if your income dropped to \(m' = \$120\)?
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Holding income and the price of good 2 constant, an increase in the price of good 1 will cause the budget line to become:
steeper
flatter
it depends on thelevel of income
it depends on theprice of good 2
Example:
Apples cost 50 cents each
Bananas cost 25 cents each
Slope of the budget line represents the opportunity cost of consuming good 1, as dictated by market prices.
In other words: it is the amount of good 2 the market requires you to give up in order to get another unit of good 1.
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If apples (good 1) cost $0.80 each,
and bananas (good 2) cost $0.20 each, what is the magnitude (absolute value) of the slope of the budget line?
You have $100 in your pocket.
You see a cart selling apples (good 1) for $2 per pound.
(more on these in the interactive lecture notes)
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BL
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PPF
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All the math we did last week holds,
but the slope of the constraint is the price ratio,
not the MRT. (Still opportunity cost!)
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"Gravitational pull" argument:
Indifference curve is
steeper than the budget line
Indifference curve is
flatter than the budget line
Moving to the right
along the budget line
would increase utility.
Moving to the left
along the budget line
would increase utility.
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Can sometimes use the tangency condition
\(MRS = p_1/p_2\), sometimes you have to use logic.
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BL1
We will be solving for the optimal bundle
as a function of income and prices:
The solutions to this problem will be called the demand functions. We have to think about how the optimal bundle will change when \(p_1,p_2,m\) change.
BL2
The consumer receives more utility per additional unit of good 1 than the price reflects, relative to good 2.
The consumer receives more
"bang for the buck"
(utils per dollar)
from good 1 than good 2.
Regardless of how you look at it, the consumer would be
better off moving to the right along the budget line --
i.e., consuming more of good 1 and less of good 2.
The consumer is more willing to give up good 2
to get good 1
than the market requires.
MRS and the Price Ratio: Cobb-Douglas
The budget line and indifference curves describe different things.
Indifference curves describe the "shape of the utility hill."
They do not change when prices or income change.
They do change when preferences change, but we usually assume preferences are fixed.
The budget line describes the boundary of affordable bundles;
we can think of it as a fence over the utility hill.
IF...
THEN...
The consumer's preferences are "well behaved"
-- smooth, strictly convex, and strictly monotonic
\(MRS=0\) along the horizontal axis (\(x_2 = 0\))
The budget line is a simple straight line
The optimal consumption bundle will be characterized by two equations:
More generally: the optimal bundle may be found using the Lagrange method
\(MRS \rightarrow \infty\) along the vertical axis (\(x_1 \rightarrow 0\))
First Order Conditions
"Bang for your buck" condition: marginal utility from last dollar spent on every good must be the same!
What happens when the price of a good increases or decreases?
What happens when income decreases?
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If your utility function is
\(u(x_1,x_2) = 4x_1 + 2x_2\),
when will you buy only good 1?
Next class, we'll derive the demand functions: that is, the optimal choice as a function of prices and income.
Notice that your optimal choice depends on the prices of goods and your income.