Question

If a consumer has Cobb-Douglas preferences, the demand for one good does not depend on the price of the other good.

True or false?

Answer 1

Ans. True

Suppose consumer consumes two goods, x and y having price p and q respectively and income of the consumer is M. The preferences of the consumer are cobb douglas funtion, so,

=> U = x^0.5y^0.5

=> Marginal utility of x, MUx = dU/dx = 0.5 * (y/x)^0.5

and Marginal utility of y, MUy= dU/dy = 0.5*(x/y)^0.5

=> Marginal rate of substitution, MRS = MUx/MUy = y/x

At equilibrium,

MRS = p/q

=> y/x = p/q

=> y = xp/q

Substituting this in budget constraint, px + qy = M, we get

px + px = M

=> x = M/2p

and y = M/2q

Thus, we get that demand for one good does not depend on the price of other good.

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