# How To Calculate Shadow Prices?

S.t.    (1)   40X + 50Y≤ 80,000   Labour constraint
(2)   40X + 30Y≤ 60,000   Capital constraint
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A company makes 2 kinds of garden chair, a Highback and a Leisure model.
Profit on the Highback chair is £40 and on the Leisure model £50. The company are planning their weekly work schedule, they want to maximise their profit. The production mix is subject to certain constraints. They must make at least 40 chairs in total per week and they can make no more than 60 of the Leisure model.
The level of production is restricted by the weekly labour availability according to the following table:

HighBack
Requirement (minutes) Leisure Requirement
(minutes)
Availability
(minutes)
Fabric Construction 20 30 2400
Frame Construction 30 20 3000
Calculate the shadow price for both fabric and frame construction
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It may be clarified here that the use of shadow prices has relevance only in case of economic analysis of projects in which social return or over all return to society as a whole from a particular investment project is evaluated. In financial analysis, on the contrary, the market prices of factors are pressed into services, regardless of their true worth or opportunity costs or scarcity values.

The simple reason is that financial analysis is concerned with the financial return to an equity participation or private return to an individual investor or financial contributor businessman, industrialist, farmer, joint stock company, public corporation etc. All these financial entities have a vital stake only in financial return to the capital contributed by them. The social return does not figure at all in their calculation or occupies only a secondary place.

In the special circumstances of the under developed countries, the use of shadow prices for unskilled labour, foreign exchange and capital is particularly recommended in the economic analysis of a projects. The calculation of shadow price of each of these factors is however a ticklish and hotly debated issue. Partial equilibrium method due to its relative simplicity and the greater accuracy, prices of each sector is determined separately while general equilibrium method establishes equilibrium among all the factors by equating their total supply to total demand.
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There are two main ways:
1. Revealed preference - consumers are faced with a choice, the final decision made created an imputed value for the externality
2. Hedonic pricing - two goods are compared which are identical apart from one suffers from an externality, the difference between the two goods is used as a proxy for the financial value of the externality
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