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115年 - 115 原住民族特種考試_三等_財稅行政:稅務法規#144526(28題)

115年 - 115 原住民族特種考試_三等_經建行政:貨幣銀行學#144525(11題)

115年 - 115 原住民族特種考試_五等_各類科:英文#144524(10題)

115年 - 115 外交特種考試_三等_外交領事人員類科英文組一、外交領事人員類科法文組、外交領事人員類科德文組、外交領事人員類科日文組、外交領事人員類科西班牙文組、外交領事人員類科阿拉伯文組、外交領事人員類科韓文組、外交領事人員類科俄文組、外交領事人員類科義大利文組、外交領事人員類科土耳其文組、外交領事人員類科葡萄牙文組:國際經濟#144523(28題)

115年 - 115 原住民族特種考試_五等_各類科:原住民族行政及法規大意#144522(40題)

115年 - 115 外交特種考試_三等_外交領事人員類科英文組一、外交領事人員類科法文組、外交領事人員類科德文組、外交領事人員類科日文組、外交領事人員類科西班牙文組、外交領事人員類科阿拉伯文組、外交領事人員類科韓文組、外交領事人員類科俄文組、外交領事人員類科義大利文組、外交領事人員類科土耳其文組、外交領事人員類科葡萄牙文組:國際公法#144521(23題)

115年 - 115 外交特種考試_三等_外交領事人員類科英文組一、外交領事人員類科法文組、外交領事人員類科德文組、外交領事人員類科日文組、外交領事人員類科西班牙文組、外交領事人員類科阿拉伯文組、外交領事人員類科韓文組、外交領事人員類科俄文組、外交領事人員類科義大利文組、外交領事人員類科土耳其文組、外交領事人員類科葡萄牙文組、外交領事人員類科國際法組:國際關係與近代外交史#144520(24題)

115年 - 115 原住民族特種考試_三等_土木工程:結構學與鋼筋混凝土學#144519(4題)

115年 - 115 原住民族特種考試_四等_會計:會計法規概要#144518(22題)

115年 - 115 原住民族特種考試_四等_土木工程:材料力學與土木施工學概要#144517(5題)

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(c) In reality, wage disparities across sectors are common. In aging economies like Taiwan, the LTC sector faces a persistent labor shortage, creating significant challenges in meeting the growing demand for care services. Explain what could be the possible reasons to the shortage, and propose policies to address the shortage. (10%)

(b) Now assume workers live for two periods: young and old. Each worker is endowed with one unit of labor time when young, supplies labor to the market inelastically during their youth, retires and consumes LTC services when old. The lifetime utility of a worker born in period \( t \) is$U^t = \ln(c_t^y) + \beta \ln(x_{t+1}),$where $c_t^y$ is consumption when young, $x_{t+1}$ is LTC service purchased when old, and $\beta > 0$ is the discount factor or the preference for old-age utility. Denote the saving of a worker when young by $s_t$. A worker's budget constraint when young and when old are:$c_t^y + s_t = w_t,$$p_{t+1}x_{t+1} = R_{t+1}s_t.$where $R_{t+1}$ is the gross return on savings, and $w_t \in \{w_{Y,t}, w_{LTC,t}\}$. Capital fully depreciates after one period of use. Let $k_t \equiv K_t/L_{Y,t}$ denote the capital intensity in the goods sector. Solve for the steady-state values for $k^*$, $p^*$ and the fractions of labor allocated to the goods sector ($L_Y/L$) and the LTC sector ($L_{LTC}/L$). Analyze how the steady-state values of $k^*$, $p^*$, $L_Y^*/L$ $L_{LTC}^*/L$ respond to an increase in $B$, $\beta$ and $\alpha$. Explain your results with economic intuition. (10%)

(a) Derive the expression for total GDP in this economy. Solve for \( w_{Y} \) and \( w_{LTC} \), i.e., the marginal product of labor in both the sectors. Also, write down the condition for both sectors to coexist in equilibrium. (10%)

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