Are Cobb-Douglas preferences homothetic?
It can also be shown algebraically that Cobb-Douglas preferences are homothetic because if XαY 1−α > (X )α(Y )1−α then (tX)α(tY )1−α > (tX )α(tY )1−α. (This is ensured mathematically be- cause the Cobb Douglass utility function is homogeneous, meaning that U(tX, tY ) = tN U(X, Y ) where N is the degree of homogeneity.)
How do you know if preferences are homothetic?
preference relation º is homothetic if and only if it can be represented by a utility function that is homogeneous of degree one. In other words, homothetic preferences can be represented by a function u() that such that u(αx) = αu(x) for all x and α > 0.
What does it mean if preferences are homothetic?
Preferences are intratemporally homothetic if, in the same time period, consumers with different incomes but facing the same prices and having identical preferences will demand goods in the same proportions.
How do you prove a function is homothetic?
A function f: C → R is homothetic if for every x, y ∈ C and t > 0, f(x) ≥ f(y) if and only if f(tx) ≥ f(ty). One consequence of the definition of homotheticity is that f is equivalent to g defined by g(x) = f(tx). Any homogeneous utility function is also homothetic.
Why do we assume homothetic preferences?
The assumption of homothetic preferences in these models provide means and tools of analysing situations where technology rather than demand factors are the main driving force of aggregate outcomes. Assuming homotheticity also makes these models more tractable for empirical implementation.
What is homothetic production function?
Homothetic functions are functions whose marginal technical rate of substitution (the slope of the isoquant, a curve drawn through the set of points in say labour-capital space at which the same quantity of output is produced for varying combinations of the inputs) is homogeneous of degree zero.
What is the meaning of homothetic?
: similar and similarly oriented —used of geometric figures.
Why does MRS decrease?
Essentially, MRS is the slope of the indifference curve at any single point along the curve. Most indifference curves are usually convex because as you consume more of one good you will consume less of the other. So, MRS will decrease as one moves down the indifference curve.
Where can I find MRSxy?
The Marginal Rate of Substitution of Good X for Good Y (MRSxy) = ∆Y/ ∆X (which is just the slope of the indifference curve).
What is the limitation of the Cobb-Douglas production function?
Since, the Cobb-Douglas (CD) function has been (and is still) abundantly used by economists because it has the advantage of algebraic tractability and of providing a fairly good approximation of the production process. Its main limitation is to impose an arbitrary level for substitution possibilities between inputs.