# Correcting Market Distortions: Shadow Prices, Shadow Wages and Discount Rates Chapter 6.

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Correcting Market Distortions: Shadow Prices, Shadow Wages and Discount Rates Chapter 6

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.

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 = P f + T P c – price gross of tax P f – price net of tax

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 C – Output increases from X e to X f – price firms retain increases from P f to P f ’ – Price consumers pay increases from P c to P c ’

Non-project demand for the firm falls from X e to X c Note that the Government requirement of X G comes from two sources: – X f - X e – units of new supply – X e - X c – units of displaced demand If 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.

→ D 1 is flatter than D 2 → D 1 is more elastic than D 2

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 inelastic

Extreme Cases

Distortionary Sudsidies Analysis is basically the same as a distortionary tax

Shadow Wage Rates Governments sometimes use discretionary fiscal policy to create jobs. If labour markets functioned perfectly market wages would reflect true opportunity cost of hiring labour for a project However, markets usually don’t function perfectly because of distortions so have to calculate the shadow price of labour. i.e. the shadow wage rate. Can draw labour for public projects from three sources: i.those employed elsewhere in the economy ii.the voluntarily unemployed iii.the involuntarily unemployed There are implications of i) to iii)

RE: i.) Those employed elsewhere in the economy: – When draw someone who already has a job into a public job, the value of the output they produced is forgone. – Measure by their marginal product of labour i.e. market wage Recall firm is a profit maximizer or cost minimizer so they expand output as long MPL exceeds the wage rate. – Denote market wage by w 1

RE: ii.) Voluntary unemployed, e.g., retired people or people in school – opportunity cost of these people is the minimum amount required to induce them to work – measure their opportunity cost by the wage the project pays them w2

RE: iii.) Involuntary unemployed people willing to work at the market wage but unable to find a job – On the one hand, can argue that this opportunity cost is zero – On the other hand, can also argue that market wage is not sufficiently large enough to induce them to work [should work for the market wage rate X] – Denote this wage by w3 – Since don’t really know what this wage is you have to make some assumptions about its values – One assumption that is used is that the value is at least 20% greater than the market wage.

Choosing and Computing a Discount Rate

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.

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.

supply of funds for investment is provided by individual saving if rate of interest > rate of time preference then save represented by Aggregate savings schedule

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 rate

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.

Market Equilibrium with Distortions

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.

Criticisms

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 resources

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(0.037)+0.05(0.0173 )=0.0437 or 4.4%

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(0.037)+0.832(0.0173)= 0.0268 or 2.7%

Rules of Thumb: United States

Rules of Thumb: Canada The 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.