Please comment if they are true or false, explaining

1.the market equilibrium will always be efficient, since the equilibrium quantity and price are the result of the exchange relations between suppliers and demanders, regardless of whether they generate the same effect privately or in society.

2.The authorities are concerned, given that they cannot find an economic interpretation of the price elasticity of energy demand. You are hired to explain why the price elasticity would be lower in summer than in winter.

3.An individual who considers 2 goods x1, x2 as complements and is indifferent when he consumes the baskets (x1, x2) equal to (2, 3) and (2, 5) is not complying with the axiom of Monotonicity or the one of Local Non-Satiation .

4.When you have an inferior good and a normal good, the Engel curve will necessarily be decreasing.

5.An increasing utility function implies that its associated indifference curves will necessarily be decreasing, while the marginal rate of substitution is always negative.

6.Studying with friends, one of them comments that regardless of whether it is a Marshallian demand or a Hicksian demand for a good, the price elasticity of demand will be the same.

7.Marshallian demands are homogeneous of degree 0 at (p, y). Similarly, the Hicksian demands are homogeneous of degree 0 in (p, u). This is because the minimization of spending is the dual problem of utility maximization, therefore, the solutions to these problems must have analogous properties to each other.

8.If an agent's reservation salary is higher than the salary offered by the market, then a reasonable decision would be for the individual to decide to participate in the labor market.