Demand function is homogeneous of degree zero, Microeconomics

Assignment Help:

Demand Function is Homogeneous of Degree Zero:

Mathematical Presentation 

we will show that demand function is homogeneous of degree zero in prices and money income. In other words, if prices and money income change proportionately, then demand for all goods (and therefore the equilibrium bundle) remain the same. Initial price set p0 = (p10, p20,...,pn0) and the money income is I0 at which commodity vector x0 is bought, where x0 = (x10, x20,...,xn0) and p0x0 = I0. Let there be another commodity set x1 = (x11, x21,...,xn1).  At prices p0 set x1 is not chosen because it is not more expensive than x0 and at that price x1 is available so x0 is revealed preferred to x1. So,  

1177_Demand Function is Homogeneous of Degree Zero.png

Consider a change in prices to p1 = (p11,...,pn1) and income changes to I1, when consumer buys x1. So x0 at that new price level is not available to the consumer and we have,  

399_Demand Function is Homogeneous of Degree Zero1.png

Let I1 = m I0 and p1 = m p0, where m is any positive number. Prices and income change in same proportion m and we have,  

1194_Demand Function is Homogeneous of Degree Zero2.png

Equations (c) and (d) contradict equations (a) and (b). Hence, we conclude that the xand x0 sets are identical and demand functions ( which are functions of prices and quantities) are homogeneous of degree zero and same proportional change in prices and income leads an individual to buy the same bundle.  


Related Discussions:- Demand function is homogeneous of degree zero

Pure monopoly, advantage dis advantage of pure monopoly

advantage dis advantage of pure monopoly

Explain how unemployment could be voluntary or involuntary, Explain how une...

Explain how unemployment could be voluntary or involuntary . Start off with a definition of the labour force and then outline the proportion of the labour force which would be

How the inflation effect on import and export of the country, How the infla...

How the inflation effect on the Import and Export of the country?  When general price level enhances in an economy, local currency is devalued. Economy has to spend more on imp

Determine the nominal reservation wage, Mikes' preferences for consumption ...

Mikes' preferences for consumption and leisure may be represented by the Utility function: u(C, L) =  ( C-200)*(L-80) . His marginal utilities of leisure and consumption are (C-200

find the equilibrium quantity and demand curve, Consider a non-renewable r...

Consider a non-renewable resource. There are two periods, now and later. The demand curve in each period (t = 1, 2) is Qt = 10 - Pt. The stock of the resource is 10 units. Extracti

Long run eq, The raspberry growing industry is a perfectly competitive indu...

The raspberry growing industry is a perfectly competitive industry. The firms in the industry have a U-shaped LAC, minimum average cost is $8 and the minimum efficient scale is 4 u

States the amount of grain, If Kansas can formed either 400 tons of wheat o...

If Kansas can formed either 400 tons of wheat or 100 tons of corn and Nebraska can formed 300 tons of corn or 200 tons of wheat then it makes sense for the two states to specialize

Derive the linear demand and supply, Suppose that the short-run world deman...

Suppose that the short-run world demand and supply elasticities for crude oil are -0.076 and 0.088, respectively. The current price per barrel is $30 and the short -run equilibrium

Supply, what happen when a supply shift to the right on a graph

what happen when a supply shift to the right on a graph

Determine the price elasticity of demand, Given the following demand and to...

Given the following demand and total cost functions for a firm P = 4500 - 0.5Q 2                     TC = 1.5Q 3 - 50Q 2 + 1000   i) the marginal profit function

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd