中级宏观经济学Lecture09.consumption
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Goldbaum (UTS)
Lecture 9
Macro 2014
11 / 26
Consumption
The consumer’s budget constraint Period 1: Income in period 1 can be used for consumption and savings y1 ≥ c1 + s (1)
There is some value Y > X such that Ut (Xt ) = Ut (Yt +1 )
β is a “discount factor” that converts future utility values to their present value equivalent so that Ut (Xt ) = Ut (Yt +1 ) = β Ut +1 (Yt +1 ) The time subscripts can be dropped from the utility function.
The value today of a future payment t periods away is β t U (X )
Goldbaum (UTS)
Lecture 9
Macro 2014
6 / 26
Interest
Using interest to measure value across time Consider $Xt as a dollar amount today Consider $Yt +1 as a dollar amount available 1 year from today At nominal interest rate i , the market value of $Xt and $Yt +1 are equivalent if:
Period 2: period 2 income plus any savings are available for period 2 consumption (1 + r )s + y2 ≥ c2 (2) Intertemporal budget constraint (ITBC): Solve (1) for s , plug into (2) c1 + c2 y2 ≤ y1 + 1+r 1+r
Y
X (1 + r ) =
⇒ ⇒ (1 + i ) = (1 + π )(1 + r ) which is closely approximated as i = π + r
Y 1+π X (1+i ) X (1 + r ) = 1+π
Goldbaum (UTS)
Lecture 9
Macro 2014
2
3
Goldbaum (UTS)
Lecture 9
Macro 2014
2 / 26
Investment
Investment should be understood as the product two parties interacting in the market for savings/investment Households balances the value of consumption today against the value consumption at some future date
Yt +1 = Xt (1 + i ) or Xt =
Y t +1 1+i
Present Discounted Value (PDV): Xt =
Yt +1 1+i
is the PDV of Yt +1
Xt represents the money equivalent in today’s dollars of the future amount, Yt +1 A market determined rate of intertemporal rate of exchange
Savings today is a decision to forgo consumption today in favor of consumption in the future Household savings represents the supply side of the investment market
Given an income stream, must decide how much to consume from current income and how much to save (or borrow)
y1 and y2 are income in periods 1 and 2 respectively. These are set exogenously. c1 and c2 are consumption in periods 1 and 2 respectively. The consumer gets to choose c1 and c2 subject to affordability constraints.
Intermediate Macroeconomics
Lecture 9 Lectured by Elham Pour Azarm
EconomiFra Baidu biblioteks Discipline Group University of Technology Sydney
Goldbaum (UTS)
Lecture 9
Macro 2014
Goldbaum (UTS)
Lecture 9
Macro 2014
4 / 26
Consumption
Goldbaum (UTS)
Lecture 9
Macro 2014
5 / 26
Personal Discounting
Discounting of future utility Standing at time t , a dollar amount $X paid today will have a certain utility value, Ut (Xt ) Standing at time t , a the same dollar amount paid one year from today will have a different value, Ut (Xt +1 ) = Ut (Xt ) In order for a future payment to have the same utility value as a current payment, the future payment will typically have to be bigger.
1 / 26
Outline
1
Consumption, Savings and Investment Discounting Simple Consumption Function 2-Period Consumption Decisions Advanced Notions of Consumption Firm’s Decision on Capital Cost and benefits of owning capital Market equilibrium
Goldbaum (UTS)
Lecture 9
Macro 2014
9 / 26
Consumption
Want to explain savings as a conscious consumer decision Gain an understanding of consumer behavior through a 2-period model of lifetime consumption and income.
Firms determine how much capital they need in order to maximize profits.
Demand side of the investment market
Interest rates are determined by market forces in order to balance savings with investment.
Normally, non-satiated consumers will use all resources on consumption c2 y2 c1 + = y1 + (3) 1+r 1+r Interpretation of ITBC: The total present discount value (PDV) of lifetime consumption is equal to the total PDV of lifetime income
Save s today. Next year will have (1 + r )s Borrowing is captured by s < 0. A household that borrows “earns” (1 + r )s next year. Since this is negative, it represents how much is owed.
t +1 for inflation at πt , the purchasing power is the equivalent of 1+ πt (in current dollars) In purchasing power, the loan was as though the lender gave up $Xt Y t +1 today and receives back 1+ πt let r be the real interest rate (measured in terms of purchasing power)
Goldbaum (UTS)
Lecture 9
Macro 2014
10 / 26
Consumption
Build on the notion of the consumer household A household can save or borrow at the same real interest rate of r .
8 / 26
Consumption
A simple notion of the the relationship between consumption and income (aggregate) ¯ + c (Y + TR ¯ − TA ¯ ) with Recall C = C
¯ = Autonomous Consumption,C ¯ >0 C c = Marginal Propensity to Consume (MPC), 0 < c < 1
Goldbaum (UTS) Lecture 9 Macro 2014 12 / 26
¯ − NX ¯ so that in the goods market From NIPA, S = Y − C − G equilibrium I (r ) = S = Y − C (Y ) − G − NX Y adjust to maintain this equality
For r ↑⇒ I ↓, then Y ↓ so that (Y − C (Y )) ↓ and S ↓ For G ↑, then Y ↑ so that (Y − C (Y )) ↑ and S stays unchanged
Goldbaum (UTS)
Lecture 9
Macro 2014
7 / 26
Interest
Interest in the presence of inflation A lender lends $Xt today and receives back $Yt +1 one year from today where Yt +1 = Xt (1 + i ). Inflation reduces the purchasing power of the $Yt +1