111年 - 111 國立臺北大學_碩士班一般入學考試試題_經濟學系：個體經濟學#146584

(a) (3%) Define Weak Axiom of Revealed Preference (WARP).

(b) (6%) A consumer chooses consumption bundles (17, 8, 5), (10, 5, 10), (12, 1, 20) when facing prices (1, 1, 2), (1, p, 1), (2, 1, 1), respectively. Suppose p is a positive integer, what value should p take to make these data satisfy WARP?

(a) \( (5\%) \) Verify the degree of homogeneity of this production function.

(b) \( (5\%) \) Calculate the elasticity of substitution for this production function.

(c) \( (5\%) \) Let \( w \) and \( r \) denote the prices for \( L \) and \( K \), respectively. Derive the demand function for \( L \) (i.e., \( L \) as a function of \( Q \), \( w \), and \( r \)).

(d) (3%) Compare your answer in (c) to a demand function for \( L \) derived from a Cobb-Douglas production function (e.g., \( Q = L^{0.5}K^{0.5} \)), which demand for \( L \) is relatively insensitive to \( w \)?

(a) \( (5\%) \) What is the producer surplus of an individual firm?

(b) \( (3\%) \) What do you know about the firm's economic profit?

(c) \( (5\%) \) What is the overall producer surplus for the market?

(d) \( (5\%) \) What are your answers to (a) and (c) when the market demand becomes \( D(P) = 150 - 5P \)?

(a) (6%) How much extra surplus does the producer capture when it can engage in first-degree price discrimination instead of charging a uniform price?

(b)(6%) Find the profit-maximizing quantity and price for block 1 \( (P{1}, Q{1}) \) and for block 2 \( (P{2}, Q{2}) \).

(c)(3%) What's the firm's producer surplus under the two-block tariff in part b?

(a) \( (4\%) \) What are the Cournot equilibrium quantities and price in this market?

(b)(3%) What would be the equilibrium price in this market if the two firms acted as a profit-maximizing cartel?

(c) \( (6\%) \) What's the Stackelberg equilibrium quantity for each firm? What's the market price?

(d)(4%) What's the profit for each firm?

(a) \( (3\%) \) What is the size of the surplus created by the price floor?

(b)(3%) Assuming the most efficient producers are active, what's the deadweight loss due to the price floor?

(c)(6%) Assuming the least efficient producers are active, what's the producer surplus (PS) under the price floor? What's the deadweight loss due to the price floor?

8. Consider a market of risk-averse decision makers, each with a utility function U = √I. Each decision maker has an income of $90,000, but faces the possibility of a catastrophic loss of $50,000 in income. Each decision maker can purchase an insurance policy that fully compensates her loss. This insurance policy has a cost of $11,600. Suppose each decision maker potentially has a different probability q of experiencing the loss.

(6%) What is the smallest value of q so that a decision maker purchases insurance?