If someone has a Cobb-Douglas utility function and no income from any source other than labor earnings, then an increase in wages will not change the amount that person chooses to work.

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The Cobb-Douglas utility function is a function that represents the utility or satisfaction that a consumer derives from consuming two goods. The function is given by U(x,y) = x^a * y^b, where x and y are the quantities of the two goods consumed, and a and b are positive constants.If a consumer has no income from any source other than labor earnings, then the consumer's budget constraint is given by I = w*L, where I is the consumer's income, w is the wage rate, and L is the amount of labor supplied.The consumer's optimal choice of labor supply is the amount of labor that maximizes the consumer's utility function subject to the budget constraint. The optimal choice of labor supply is given by L* = (a*I)/(w*(a+b)).If the wage rate increases, then the consumer's income will increase. This will lead to an increase in the consumer's optimal choice of labor supply. Therefore, an increase in wages will change the amount that the person chooses to work.

If Someone Has a Cobb-Douglas Utility Function and No Income