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115年 - 115 國營臺灣鐵路股份有限公司工務處從業人員甄試_第 10 階-助理事務員-企劃研析(工程管考實務):運輸學概要#145869(50題)

115年 - 115 國營臺灣鐵路股份有限公司工務處從業人員甄試_第 11 階-服務員-事務管理(身心障礙):事務管理大意#145868(50題)

115年 - 115 國營臺灣鐵路股份有限公司工務處從業人員甄試_第 10 階企劃研析(工程管考實務):作文#145867(1題)

115年 - 115 國營臺灣鐵路股份有限公司工務處_從業人員甄試試題_第 10 階、第 11 階各類科【第 10 階企劃研析(工程管考實務)類科除外】:作文#145866(1題)

115年 - 115 國營臺灣鐵路股份有限公司工務處_從業人員甄試試題_第 8 階、第 9 階各類科:作文#145865(1題)

115年 - 115 國營臺灣鐵路股份有限公司工務處_從業人員甄試試題_第 10 階-助理技術員-養路工程、養路工程(維修實務):鐵路工程大意#145864(50題)

115年 - 115-3 合作金庫新進人員甄試試題:綜合科目(會計學概要.貨幣銀行學.票據法.銀行法)#145863(73題)

115年 - 115年 - 115-3 合作金庫商業銀行_新進人員甄試試題_一般金融人員:含會計學、貨幣銀行學、法律常識(票據法/銀行法)#145862(70題)

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115年 - 105 國立嘉義大學_碩士班(甲組)招生考試試題_木質材料與設計學系:木材化學#145849(11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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