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115年 - 115-2 專技高考_醫事放射師:基礎醫學(包括解剖學、生理學與病理學)#142560(80題)

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115年 - 115-2 專技高考_醫師(一):醫學(二)(包括微生物免疫學、寄生蟲學、藥理學、病理學、公共衛生學等科目知識及 其臨床之應用)#142550(100題)

115年 - 115-2 專技高考_醫師(一):醫學(一)(包括生物化學、解剖學、胚胎及發育生物學、組織學、生理學等科目知識及其臨床之應用)#142548(100題)

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115年 - 115-2 專技高考_牙醫師(一):牙醫學(一)(包括口腔解剖學、牙體形態學、口腔組織與胚胎學、生物化學 等科目及其臨床相關知識)#142544(80題)

115年 - 115-2 專技高考_醫事檢驗師:臨床血清免疫學與臨床病毒學#142543(80題)

115年 - 115-2 專技高考_醫事檢驗師:生物化學與臨床生化學#142541(80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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