(1) Write out the Lagrangian and find the first-order conditions for the visitor’s
utility-maximization problem. Give an economic interpretation for the first-order
conditions. (20%)
Let the market demand for widgets be described by Q = 1000 − 50P . Suppose further
that widgets can be produced at a constant average and marginal cost of $10 per unit.
(1) Calculate the market output and price under perfect competition and monopoly
respectively. (10%)
Let the market demand for widgets be described by Q = 1000 − 50P . Suppose further
that widgets can be produced at a constant average and marginal cost of $10 per unit.
(2) What is the elasticity of demand in the competitive equilibrium by the point
elasticity of demand? (5%)
Let the market demand for widgets be described by Q = 1000 − 50P . Suppose further
that widgets can be produced at a constant average and marginal cost of $10 per unit.
(3) What is the elasticity of demand in the monopoly equilibrium by the point elasticity
of demand? (5%)
(1) Find an expression for the MRTS, and show that isoquants are strictly convex to the
origin. (10%)
(2) Show that f is homogenous, and find its degree of homogeneity. (10%)
(3) Find the elasticity of substitution between the inputs. (10%)
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