ECON10A_12 - 1 Discounting Consumption in future is not as...

1/4/2008
1
Review – Supply of Capital

1/4/2008
2
Discounting

Consumption in future is not as valuable as
consumption today

Interest rate r is one way to capture this

$1 today→$(1+r) next period

$1 next period→$1/(1+r) today

1/4/2008
3
Budget Constraint - Algebraically

I
1
income in period 1

I
2
income in period 2

Express total income in
present dollars: I
1
+ I
2
/(1+r)

Budget line:
c
1
+ c
2
/(1+r)= I
1
+ I
2
/(1+r)
p
1
x
1
+p
2
x
2
= I
1
+ I
2
/(1+r)

p
1
=1, p
2
=1/(1+r)

“Price” of $1 now is $1 now

“Price” of a future dollar of
consumption is 1/(1+r) dollars
now.

Give up 1 units present
consumption→
Can consume (1+r) in future

Budget line:
c
1
+ c
2
/(1+r)= I
1
+ I
2
/(1+r)
C
1
C
2
I
1
I
2
Slope=
-(1+r)

1/4/2008
4
Indifference Curves

U(c
1
, c
2
)

MRS=mu
1
/mu
2

Diminishing MRS

C
1
C
2
I
1
I
2

1/4/2008
5
Putting It All Together - graphically

Max U(c
1
,c
2
)
s.t. c
1
+c
2
/(1+r) = I
1
+I
2
/(1+r)

Tangency Condition

Optimum occurs where:
Slope of indif cuirve =
Slope of budget line


Budget condition

Optimum must be on
budget line

c
1
+c
2
/(1+r) = I
1
+I
2
/(1+r)

C
1
C
2
I
1
I
2
r
c c mu
c c mu
+ = 1
) , (
) , (
2 1 2
2 1 1
C
1
*
C
2
*

Question 1

If interest rate is 5%, what is c
2
*?

A. 79 B. 80 C. 85 D. 100 E. Can’t Tell
1/4/2008
6
c
1
c
2
100
100
120
c
2
*

Question 1

If interest rate falls, c
2
* will

A. Rise B. Fall C. Can’t tell
1/4/2008
7
c
1
c
2
100
100
120
c
2
*

1/4/2008
8
Supply of Goods and Services

1/4/2008
9
Overview

We learned how households choose quantity of a
given commodity they will consume, given prices
and income.

(Quantity demanded)

But goods must be produced (i.e., supplied).

We have yet to see how firms choose the quantity of
goods they will produce, given prices and costs.