Final answer:
The question involves calculating the income elasticity of good x1 given a utility function U(x1; x2) = Min(x1; x2). The demand function for x1 is derived from the budget constraint, and then its derivative with respect to income I is used to determine the income elasticity.
Step-by-step explanation:
The student is asking about the income elasticity of good x1 when the utility function is given by U(x1; x2) = Min(x1; x2). The budget constraint for a consumer is I = p1*x1 + p2*x2, where I is income and p1 and p2 are prices of goods x1 and x2, respectively. Because the utility function is a perfect substitutes utility function, the consumer will spend all of their income on the good that provides the most utility per unit of money, which means the consumer will equalize the two goods until either the budget runs out or the prices change.
To find the demand for x1, one must set up the budget constraint and solve for x1 in terms of I, p1, and p2. Once the demand function is identified, the income elasticity of x1 can be determined by taking the derivative of the demand function with respect to income I, and then dividing by the original demand function, as elasticity is a measure of proportional change.