Final answer:
The Marshallian demand functions for goods x1 and x2 can be found by equating the ratio of the prices to the ratio of marginal utilities and incorporating the consumer's budget constraint. For the given utility function and prices, the calculation involves derivatives and simple algebra to solve for the demands of both goods.
Step-by-step explanation:
To compute the Marshallian demand functions for the goods x1 and x2, based on the consumer's utility function u(x₁, x₂)=2log x₁+x₂ and the given prices p₁=2, p₂=1, we follow the rule that the ratio of the prices of the two goods should equal the ratio of their marginal utilities. The first step is to find the marginal utilities of x1 and x2.
The marginal utility of x1 (MU1) is the derivative of the utility function with respect to x1, which is (2/x₁). The marginal utility of x2 (MU2) is the derivative with respect to x2, which is simply 1. Using the rule that MU1/P₁ = MU2/P₂, we can set up the equation:
(2/x₁) / 2 = 1 / 1
This simplifies to x₁ = 2.
The next step is to determine the consumer's budget constraint, which is given by the equation px₁ + qx₂ = M, where M is the income of the consumer. Using x₁ = 2 and substituting into the constraint, we find the demand for x2 in terms of income.
In general, the demand functions show how many units of each good the consumer will buy based on their income and the prices of the goods. The specific Marshallian demand functions can then be derived from these relationships.