115年 - 115 國立臺北大學_日間學士班轉學生招生考試試題_財政學系日間學士班2年級：經濟學#147740

(a) Derive the marginal revenue (MR) function and the marginal cost (MC) function. \( (5\%) \)

(b) Determine the profit-maximizing output level \( (Q^{*}) \) and price \( (P^{*}) \). Clearly show all intermediate steps. \( (10\%) \)

(c) Suppose the government imposes a per-unit tax of \( t = 5 \) on the monopolist's output. Determine the new profit-maximizing price and quantity, and compare the new price and quantity with the pre-tax equilibrium. (10%)

(d.1) Derive the profit function for each firm and obtain the reaction function of each firm. \( (5\%) \)

(d.2) Solve for the Cournot equilibrium outputs \( q_{1}^{*} \) and \( q_{2}^{*} \). (5%)

(d.3) Determine the total market output \( Q^{*} \) and the equilibrium market price \( P^{*} \). (5%)

(d.4) Compare the Cournot equilibrium with the monopoly outcome in terms of output, price, and profit. Explain the economic intuition for why moving from monopoly to duopoly affects these outcomes. (10%)

(a) Explain the income effect and substitution effect of an increase in the real wage on labor supply. (Please provide detailed economic intuition; no mathematical derivation is required.) (10%)

(b) Solve for the worker's optimal consumption \( C^* \) and optimal labor supply \( N^* \). (5%)

(c) Analyze how the optimal labor supply \( N^* \) responds to: (i) an increase in the real wage \( w \); and (ii) an increase in the preference parameter \( \beta \). Clearly explain both the direction of change and the underlying economic intuition. (10%).

(a) Derive the steady-state level of capital per worker \( k \) and the steady-state output per worker \( y \), where \( k = K / N \) and \( y = Y / N \). (15%)

(b) Determine the long-run growth rates of output per worker \( y \) and total output \( Y \). Based on your results, explain why the Solow model is classified as an exogenous growth model. (10%)