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Which of the following is true about the Hessian matrix of a function f(x,y)?

It is always invertible

It is always diagonal

Its determinant is always positive

It is always symmetric

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Law of returns to scale indicate that for this law to operate, factor proportions must be ________ at same level.

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In a Hessian matrix of a function f(x,y), the determinant of the Hessian matrix (det(H)) represents:

The second-order derivative of f

The Jacobian determinant of f

The discriminant used in second derivative tests

The first-order derivative of f

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Jacobian is used for:

Second order differentials

First order differentials

First order partials

Second order partials

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How does a lump-sum tax affect marginal cost (MC)?

First increases, then decreases MC

No effect on MC

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In the Lagrange Multiplier method, the term λ represents.

The shadow price of relaxing the constraint

The optimal solution to the objective function

The second derivative of the function

The elasticity of substitution

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If u, v, w are not independent functions of independent variables x, y, z then

∂(x,y,z)/ ∂(u,v,w) = 0

∂(u,v,w)/ ∂(x,y,z) = 0

∂(x,y,z)/ ∂(u,v,w) = 1

∂(u,v,w)/ ∂(x,y,z) = 1

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Constrained optimisation uses ________ determinant to check ______ conditions.

Hessian, first-order

None of the above

Bordered hessian, first-order

Hessian, second-order

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A firm in a perfectly competitive labor market is a:

Bilateral negotiator

Monopoly employer

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For giffen goods, the relationship between price and quantity is.

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