# Demand: Derivation of Demand Curve from Hicksian Substitution Effects

A popular saying goes like, â€œif you teach the words demand homework answers and supply to a parrot, it learns everything about economicsâ€. All of us, who have taken up economics as a subject to pursue in graduation know this isnâ€™t true.
Economics is more than demand and supply, however, these two concepts forms the very foundation of the subject Economics.
The renowned researchers, who relentlessly worked on expanding the concept of demand and supply and brought it within the reach of common students, are Alfred Marshal and John R. Hicks.
Each of them has a different outlook towards maximization of utility within budget constraint. Economics is built on the theory of maximization of utility in spite of a fixed budget.
Utility
Utility is a concept of usefulness a consumer obtains from consumption of goods and implementation of services. Utility is a measurable concept which is defined as a function of income and price of the goods and services. A consumer always tries to maximize his utility given a fixed income and pre-determined price of the product.
In economics we represent maximum utility as follows:
Xi* = xi (Px1,Px2,â€¦..Pxn, I) i=1â€¦n
In a two product study,
X*= X(Px, Py, I) ; Y* = Y(Px,Py,I)
These utility functions go on to formulate the demand curve for goods and services of an individual. If Px, Py and I is known we can calculate the optimal X*. Optimal X* denotes the maximum quantity of goods and services demanded by an individual for a given utility function.
Hicks has formulated a demand curve based on dual demand theory which sets a target level of utility and works around to minimize the cost associated with it.
Hicksian demand curve is the relationship between price of a good and the demand for the same good by individual. These demand homework answers assignment can be done with the help of online experts.
Assumptions of Hicksian demand curve:

• Prices of other goods are constant and do not change or affect our theory
• Utility level is constant
• Income level is constant
• Taste and preference level is assumed to remain constant

Purchasing power parity is maintained throughout the formulation of Hicksian demand curve.
Given the assumptions, we plot all our theories in following graph
If I = PxX+PyY then 2I = 2 PxX+ 2PyY
Plotting it against budget constraint, 1/Px and 1/Py will not change if both numerator and denominator is multiplied by any constant.
With 0 change in taste and preference, there is no effect on the movement of indifference curve and hence X* and Y* remains unchanged. Even inflation fails to affect the choice of goods. With all these complicated concepts you can surely complete your assignments with ease with the help of demand homework answers.
Change in income
As we have assumed prices not to change, changes in income shifts the budget constraint parallel. Slope of budget constraint will remain same. Ceteris paribus and preference, this is how we depict the changes in income.
Change in prices
A change in price ratio (Px/Py) is associated with a change in slope of budget constraint and change in MRS i.e. marginal rate of substitution at new optimal point. At optimal point
MRS = Px/Py
In the above diagram, Px decreases to Pxi thus shifting the movement from A to B. The total effect is DX*. In economics we divide the total effect into

• substitution
• income effect

Substitution effect- is the change in optimal utility X* while moving from A to C.
Income effect- is the change in utility X* while moving from C to B.
The diagram is prepared with an assumption of normal good where DX/DI >0.
Marginal rate of substitution
This is a rate which consumer is willing to sacrifice number of units of good for of one unit of another good and service while keeping the utility constant. At equilibrium marginal rate of substitution is identical.
Summary of substitution and income effects

• It is caused by change in Px/Py
• With lower Px, price ratio is smaller and new tangency point is at a smaller MRS
• Substitution effect is measured by holding the real income or U constant
• The new price ratio I.e. movement from A to C will measure the substitution effect
• For a given price change DPx the magnitude of substitution depends on the availability of goods in the market
• Income effect, on the other hand is represented by movement to a higher utility curve i.e. U1 to U
• Decrease in prices is associated with increase in purchasing power
• Income effect is depicted by change in X* while going from C to B
• Magnitude, however, depends on the quantum of fund spent on X

Sum of income and substitution effect comprise a change in price denoted by DX*. Two effects are complementary in case of normal goods where DX/DI >0.
Based on our analytical theory of income and substitution effect, we are now equipped to formulate the individual demand curve.
Demand functions
X1* =X1(Px1,Px2,â€¦â€¦â€¦.Pxn,I)
Xn*=Xn(Px1,Px2,â€¦â€¦â€¦..Pxn,I)
In a two-good world the individual demand function is derived as
X*=X(Px,Py,I)
Y*= Y(Px,Py,I)
Considering preferences, income and Py constant, we get variable Px in demand curve space plotting it in a graph of X and Px axes.
Successive price declines leads to larger optimal quantity of X in case of normal goods where utility is directly proportional to number of units consumed and DX/DI >0
The individual curves in the below diagram does not cross paths as they belong to the same individual. The below diagram depicts the formulation of demand curve from HIcksian theory.
Income compensated demand curve reveals substitution effect of changes in Px while Py,, preferences and utility are held constant. Compensated demand curve always depicts a negative slope as substitution effect is always negative when MRS is diminishing. Compensated demand curve is steeper than non-compensated Marshallian demand curve for a normal good.
Sometimes it becomes difficult to understand such concepts in Economics. Therefore, whenever I face a problem in completing demand homework answers, I always take online help. These online services provide you with assignments done by experts in their respective field. Therefore, donâ€™t worry and take help from these online experts to complete your project.

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