Correcting Market Distortions: Shadow - PowerPoint Presentation

Slide1

Correcting Market Distortions: Shadow Prices and Discount Rates

Chapter 6Slide2

Observed

market prices sometimes reflect true cost to society. In some circumstances they don’t because there are distortions which prevent market prices from conveying true economic values

.

When

this occurs have to correct observed price to calculate the shadow price.

Types

of distortions include taxes, subsidies & other forms of gov’t intervention.

In

competitive markets

D

represents marginal benefits to society and supply curve social costs. Social costs are equal to private costs. Likewise private benefits equal social benefits.Slide3

A Market with a Per Unit Tax

Suppose have a market for good but price observed for the good includes a per unit tax, here price consumers pay is not the price the firms keeps.

T – is the

tax

P

c = Pf + T Pc – price gross of taxPf – price net of taxSlide4

Project Demand with a Per Unit Tax

Suppose

there’s a project

that

requires the good as an input

.Demand for the good increases leads to new equilibrium at point COutput increases from Xe to Xfprice firms retain increases from P

f

to P

f ’Price consumers pay increases from Pc to Pc’Slide5

Non-project

demand for the firm falls from

X

e

to

XcNote that the Government requirement of XG comes from two sources: Xf - Xe – units of new supply

X

e

- Xc – units of displaced demandIf market weren’t distorted by the tax, there would not be a problem

because

consumers

marginal benefit would equal the firms marginal costs, this not the case

here because of tax

(the competitive output should be

at

X

f

)

The tax

has driven a wedge between consumers’ and firms’ valuation of this input.Slide6

The tax creates a problem for someone trying to value the input because the market outcomes are distorted by the tax.

What

the shadow price

does is try to take the distorted prices and correct them for the distortion to get a valuation/price that is distorted.

In this example the shadow price takes

a weighted average of the opportunity costs of the two sources of the gov’t’s input requirement.  For example, Suppose the gov’t needs XG units of X to complete the project, can calculate PG

the shadow price as either

:

or

Where P

f

– price net of tax and Pc – is the price gross of tax (Pc = Pf +T)

 Slide7

An alternative expression of the shadow price in the previous example uses

elasticities

,where

is the elasticity of supply and

is the elasticity of demand

The shadow

price P

G

will depend critically on

elasticities

; elasticities will determine how big increases are in new demand as well as how big is displaced demand.  Recall that the elasticity determines the slope of the demand and supply curves.A more elastic demand(supply) curve will be flatterA more inelastic demand(supply) curve will be steeper  Slide8

→ D

1

is flatter than D

2

→ D

1 is more elastic than D2Slide9

Note that in general the shadow

price will fall between gross – of – tax and net – of – tax

price.

However, there are some special cases

where the shadow price takes on specific values.These extreme cases occur when the demand is prefectly elastic and inelastic and supply is perfectly elastic and inelasticSlide10

Extreme CasesSlide11

Distortionary Subsidies

Analysis is basically the same as a distortionary taxSlide12

Choosing and Computing a Discount Rate

Recall the NPV =

, where r is the discount rate and B and C represent benefits and costs, respectively.

The NPV will depend on r as well as benefits and costs.

a smaller discount rate will lead to larger values of the NPV, large values of

the discount

rate lead to smaller values of the

NPV

a discount rate of 0 means that society weights the future equally to the present, thought to be “altruistic” discount rate

 Slide13

Marginal rate of time preference

Consider whether someone wants a $1 today versus tomorrow

Whether someone picks to have the $1 today or tomorrow reflects their time preference, or how they trade off between these alternatives

For example, suppose you have the choice of $1000 today or $1200 one year from today, if you pick $1000 today then your rate of time preference is 20%; you would have a stronger preference for having something today.Slide14

Can formalize the idea of time preference and choosing between today and tomorrow with the following model.

Suppose individuals choose between consumption today and tomorrow, denoted

and

subject to a lifetime budget constraint.

Assume that individuals have preferences over consumption today and tomorrow

 Slide15

The individual’s problem can be written as

where

is the interest rate and T is the present value of income over the individual’s lifetime (periods 1 and 2 in this example).

We’ll discuss the solution to this problem in graphical terms,

 Slide16
Slide17

Absolute value of slope of the indifference curve measures

the rate at which individuals are

indifferent between

substituting current consumption for

future consumption, i.e., the

MRS between consumption this year and consumption next year, where and

is the marginal rate of time preference.

An equilibrium for this problem is where the rate at which people are willing to trade consumption today and tomorrow equals the price of moving consumption allocations, i.e., the interest rate

 Slide18

An equilibrium, will occur when the indifference curve is tangent to the budget line, i.e., where

If you can freely borrow then you can shift consumption to the future until the MRTP falls to the interest rate you must pay

If

then save and reduce consumption today

If

then borrow and increase consumption today

In a prefect capital market

 Slide19

Investment

demand

- Looks

at firms making investment decisions

-

Assumes perfect capital markets- A firm has a variety of investment projects to select from which have different rates of return associated with them.Slide20

supply of funds for investment is provided by individual saving

if rate of interest > rate of time preference then save

represented

by Aggregate

savings scheduleSlide21

Market equilibrium occurs where supply of savings schedule equals the demand for investment funds, where rate of return equals the rate of time preference; the equilibrium point is the market interest rateSlide22

The previous equilibrium is based on the assumption of prefect capital markets.

Generally, the real world is not comprised of perfect capital markets since there are distortions, e.g., taxes

,

risk, gov’t

borrowing,

which all drives wedges between market and social outcomes, and, consequently, society can end up with under investment.Slide23

Market Equilibrium with DistortionsSlide24

On previous slide

and

represent investment demand and supply of funds without taxes

Introduction of taxes (both corporate and personal) shifts back the investment demand and supply of funds curves, denoted by

and

With taxes the market clearing interest rate would be

The marginal return on investment before taxes would be

, the opportunity cost of forgone investment

The marginal rate of return on savings after taxes would be

 Slide25

Suppose the government undertakes a new project/program that it funds by borrowing.

This would shift out the demand for funds,

shifts out to

’

Private sector investment falls by

crowding out effect

 Slide26

Arnold

Harberger

using this framework suggests the following estimate of the

social discount rate:

Some empirical evidence suggests that savings is not very sensitive to interest rates, which implies that the savings schedule would be relatively inelastic (i.e., vertical), so that

and

and

, which implies that

 Slide27

Another approximation to social discount rate would be

Some

argue

in favour

of

as an approximation to social discount rate because social

discount rate should be rate at which individuals should be willing to postpone a small amount of consumption for future consumption

.

 Slide28

As with shadow prices, the marginal rate of time preference and the rate of return on capital can be distorted.

The distortions can include taxes, inflation and risk (default or bankruptcy)

Like shadow prices, we can take observed interested rates and correct them for the various distortions.Slide29

Computing

proxies

for a rate of return on low risk private sector investments before taxes

but after

correcting for

inflation

Suggests that we can take an observed interest and correct/adjust it to get an estimate of

Want to use a low risk corporate bond, so it would have a lower default risk and adjust it for taxes and inflation

Three steps in computation, assume that corporate bond rate is 6.86%, corporate tax rate is 35% and inflation rate is 3.92%:

 Slide30

Computing

: An Example

Figure out before return

2. Adjust for inflation

3. Adjust for bias in CPI

 Slide31

Computing

proxies for a

rate of time preference after

correcting for

inflation and taxes

Suggests that we can take an observed interest and correct/adjust it to get an estimate of

Want to use a

government

bond,

and a higher level of government, e.g., Federal first, provincial second, and lastly local, so

it would have a lower default risk and adjust it for taxes and

inflation

Three steps in computation assume that interest on government bond is 6.77%, personal tax rate is 30% and inflation rate is 3.92% Slide32

Computing

: An Example

Figure out after tax return

0.0474

2. Adjust for inflation

3. Adjust for bias in CPI

 Slide33

Criticisms

tends to produce large discount rate

estimates; computations are based on using

corporate bond, which may have a risk premium (e.g. firm may

go bankrupt

, investors want a higher return to cover this)

produces discount rate that are

too

low; individuals may not properly account for the long run effects of infrastructure programs on future generations

 Slide34

Weighted Social Opportunity Cost of Capital (WSOC)

An alternative approach for computing the social discount rate.

Takes the perspective the discount rate should reflect social opportunity cost of the resources required for a project, with weights based

based

on the relative contributions of the different sources of resourcesSlide35

The weighted social opportunity cost of capital can be computed as

,

where a

is

the proportion of the projects resources that displace private

investment, b is the

proportion of resources that are financed by borrowing from

foreigners, (

1-a-b

) is the

proportion of resources displacing domestic

consumption, and

is the government's real long-term borrowing

rate  Slide36

Since

We already know how to compute

and

, but not

; However,

is relatively straightforward to compute.

Recall that

is the government’s real long term borrowing rate, so all we need to do is adjust a nominal return government bond for inflation to obtain

 Slide37

Computing

Only two steps are need to compute

. (Figures continue from previous example)

Adjust for Inflation

Adjust for Bias in CPI 0.0268+0.01=0.0368

Note: there is no adjustment for taxes because the government doesn’t pay taxes to itself.

 Slide38

are relatively easy to compute based on available interest rate data

The weights, i.e., a, b and (1-a-b) are harder to determine

In a Canadian context, Jenkins suggested using the following

values:

a=0.75 and b=0.20,which

suggest that WSOC=0.75(0.0738)+

0.2(0.0368)+

0.05(0.0173)=

0.0636 or about 6.4%

 Slide39

On the other hand, Burgess suggests

that

for Canada a is likely to be between 0.26 and 0.32, b is between 0.55 and 0.64 and (1-a-b) is likely to be between 0.1 and 0.13. Picking the smaller value of a and the bigger value of b

produces a smaller value of WSOC; e.g., WSOC=0.26(0.0738

)+

0.64(0.0368)+0.05(0.0173)=0.0436 or 4.4%Slide40

As

another example, Suppose have a project that is financed exclusively with taxes, then b=0. The weight should represent the proportion of taxes that reduce investment and 1-a-b should represent the proportion of taxes that reduce consumption. One can obtain an estimate of a with the ratio of gross fixed investment to real GDP

. Recently, this ratio was computed as 16.8%, so that WSOC=0.168(0.0738

)+

0.0(0.0368)+

0.832(0.0173)=0.0268 or 2.7%Slide41

Rules of Thumb: United States

What do policy makers use in practice?

In the United States the Office

of

Budget Management

used a real discount rate of 10 percent during the 1970s, but had lowered this estimate to about 7 percent by 1992. Recently, the Congressional Budget Office and the General Accounting Office have used the approach to get a discount rate of about 2 percent. Municipalities in the United States tend to use discount rates of 3 percent with sensitivity analysis between 0 and 7 percent.

 Slide42

Rules of Thumb: Canada

T

he

Federal Treasury Board Secretariat has recommended from about 1976 to the late-1990s, a discount rate of 10 percent, with a sensitivity analysis at 5 and 15 percent. But they recommend much lower discount rates (0 to 3 percent) for health or environmental cost benefit analysis.

More recently, the Treasury Board Secretariat (recommends) a discount rate of about 8 percent, with a sensitivity analysis of 3 and 13 percent.

The Treasury Board Secretariat also estimates the social rate of time preference of about 3 percent.