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115年 - 115 專技高考_專利師(選試專業英文及工程力學)、專利師(選試專業英文及生物技術)、專利師(選試專業英文及電子學)、專利師(選試專業英文及物理化學)、專利師(選試專業英文及工業設計)、專利師(選試專業英文及計算機結構):專業英文#143698(28題)

115年 - 115 專技高考_專利師(選試專業英文及工業設計)、專利師(選試專業日文及工業設計):工業設計#143697(8題)

115年 - 115 專技高考_專利師(選試專業日文及工程力學)、專利師(選試專業日文及生物技術)、專利師(選試專業日文及電子學)、專利師(選試專業日文及物理化學)、專利師(選試專業日文及工業設計)、專利師(選試專業日文及計算機結構):專業日文#143696(27題)

115年 - 115 專技高考_專利師:專利審查基準與實務#143695(22題)

115年 - 115 專技高考_專利師:專利法規#143694(22題)

115年 - 115 專技高考_會計師:公司法、證券交易法與商業會計法#143693(30題)

115年 - 115 專技高考_專利師:專利行政與救濟法規#143692(25題)

115年 - 115 專技高考_會計師:高等會計學#143691(46題)

115年 - 115 專技高考_專利師(選試專業英文及物理化學)、專利師(選試專業日文及物理化學):物理化學#143690(12題)

115年 - 115 專技高考_會計師、不動產估價師、民間之公證人:國文(作文)#143689(2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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