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

科目：研究所、轉學考(插大)◆個體經濟學 | 年份：111年 | 選擇題數：0 | 申論題數：22

試卷資訊

所屬科目：研究所、轉學考(插大)◆個體經濟學

選擇題 (0)

申論題 (22)

1. (5%) Suppose a consumer with a monthly income of $600 is choosing from the following mobile phone plans to maximize his utility.

Plan 50: $50 per month to use up to 300 units per month, $0.5 for each additional unit beyond 300 units, and $0.2 for each additional unit beyond 500 units.

Plan 80: $80 per month to use up to 600 units per month and $0.4 for each additional unit beyond 600 units.

Illustrate in a figure a case in which the consumer is better off choosing Plan 80.
2. (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?
3. Given a production function $$Q = \sqrt{(L + K)}$$, answer the following questions:

(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 \( w \)?
4. Suppose there are 80 identical competitive firms, each faces the same short-run total cost function $$\mathrm{STC}(Q) = 96 + 2Q^2$$, and assume all its fixed costs are sunk. Let the market demand equals $$D(P) = 360 - 4P$$, answer the following questions:

(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 \(D(P) = 150 - 5P\)?
5. Suppose Max is a profit-maximizing monopoly firm that sells a well-designed chair. The firm faces the demand curve $$P = 28 - 0.5Q$$.

I. If the total cost for producing Q units of output is \(\mathrm{TC} = 24 + 1.5\mathrm{Q}^2\). The fixed cost is sunk, and the marginal cost curve is \(\mathrm{MC} = 3\mathrm{Q}\).
(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?
II. If the marginal cost for each chair is \( \mathrm{MC} = \$ 4 \), and there is no fixed cost. Suppose Max wants to improve its profit by implementing block pricing (assuming just 2 blocks), answer the following questions:
(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?
6. Suppose there are 2 firms in oligopoly market, and the market demand is P = 50 - Q, and MC = 10 + Q₁, i = 1, 2.

(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?
Suppose now the two firms become Stackelberg duopolists in which Firm 1 is a leader and Firm 2 a follower. Assuming that the market demand is the same as before, but the marginal cost for both firms is now MC = $20. If the follower takes the leader's output as fixed at Q₁, answer the following questions:

(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?
7. Suppose that the market for corn is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as P = 10 - Qᵈ; the supply curve is P = 0.25Qᵗ. Quantity is expressed in millions of bushels. Now suppose that the federal government imposes a price floor of $3 per bushel of corn. Answer the following questions:

(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?