臺灣水庫清淤影響自來水市場經濟福利之研究

A Study of Dam Sediment Removal in Taiwan Affect Economic Welfare of Tap Water Market

劉昭宏(Chao-Hung Liu)

指導教授 ： 孫立群

國立臺灣大學/生物資源暨農學院/農業經濟學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00316

摘要

臺灣地區水庫平均淤積率達33%，清淤成本對於供水資本的比例很高，水庫清淤會改變自來水的價格彈性，進而改變Cobb Douglas生產函數及自來水的供給函數。本研究由Solow生產函數引申出自來水的要素需求，以推求臺灣地區自來水的需求函數，並藉由Cobb Douglas生產函數推導自來水的供給函數，以建立在完全競爭市場之下及政府價格管制之下的自來水供需模型，並輔以最大供給水量限制，實証出臺灣地區水庫清淤前後，自來水的均衡及非均衡價量、消費者剩餘、生產者剩餘、經濟福利及其損失或差異。
2010年，不清淤時，在政府價格管制之下，非均衡時的經濟福利為4,182億元，經濟福利損失為6,242億元，最大供給水量限制之下的經濟福利為6,754億元，經濟福利差異為2,572億元；在完全競爭市場之下，非均衡時的經濟福利為4,335億元，經濟福利損失為3,750億元，最大供給水量限制之下的經濟福利為6,882億元，經濟福利差異為2,547億元。
2010年，不清淤時，在政府價格管制之下，與在完全競爭市場之下比較，非均衡時的經濟福利少了153億元，減少3.53 %，最大供給水量限制之下的經濟福利少了128億元，減少1.86 %，經濟福利差異多了25億元，增加1.77 %；均衡時的經濟福利多了2,339億元，增加28.93 %，經濟福利損失多了2,492億元，增加66.45 %。
2010年，清淤10億立方公尺後，與不清淤時比較，在政府價格管制之下，非均衡時的經濟福利增至6,679億元，增加59.70 %，經濟福利損失減至3,745億元，減少40.00 %，最大供給水量限制之下的經濟福利不變，經濟福利差異減至75億元，減少97.08 %；在完全競爭市場之下，非均衡時的經濟福利增至7,050億元，增加62.63 %，均衡時的經濟福利增至8,177億元，增加1.58 %，經濟福利損失減至1,127億元，減少69.95 %，最大供給水量限制之下的經濟福利增至7,128億元，增加3.57 %，經濟福利差異減至78億元，減少96.94 %。
2010年，清淤10億立方公尺後，在政府價格管制之下，與在完全競爭市場之下比較，非均衡時的經濟福利少了371億元，減少5.55 %，經濟福利損失多了2,618億元，增加232.30 %，最大供給水量限制之下的經濟福利少了374億元，減少5.25 %，經濟福利差異少了3億元，減少3.85 %。
2010年，不清淤時，在政府價格管制之下，非均衡時的經濟福利，比完全競爭市場之下，均衡時的經濟福利少了3,903億元，損失比率為77%，與清淤10億立方公尺後比較，減至1,498億元，損失比率減至46%。
2010年，不清淤時，在政府價格管制之下，有最大供給水量限制時，非均衡時的經濟福利，比在完全競爭市場之下，有最大供給水量限制時，少了2,700億元，差異比率為37%，與清淤10億立方公尺後比較，減至449億元，差異比率減至6%。
2010年，清淤10億立方公尺後，在政府價格管制之下，現行水價上漲至每立方公尺20元時，與未上漲比較，經濟福利損失由3,745億元降至1,972億元，損失比率由36%降至24%；有最大供給水量限制時，經濟福利差異由75億元降至64億元，差異比率由6%降至1.014%。
簡而言之，不論是在政府價格管制之下的清淤量增加或者是現行水價上漲，還是在完全競爭市場之下的清淤量增加，經濟福利損失或差異皆會減少。

關鍵字

水庫 ； 淤積 ； 清淤 ； 自來水 ； 水市場 ； 水價 ； 價格彈性 ； 生產函數 ； 需求函數 ； 供給函數 ； 消費者剩餘 ； 生產者剩餘 ； 經濟福利 ； 經濟福利損失 ； 經濟福利差異

並列摘要

The average sedimentation rate of dams in Taiwan reaches about 33%, whereas the cost of sediment removal accounts for a high proportion in assets of water supply. Dam sediment removal tends to change the elasticity of tap water pricing while changing the Cobb Douglas production function and the supply function of tap water. The study derives the factor demand for tap water from Solow production function, thereby to infer the demand function for tap water in Taiwan in addition to derive the supply function of tap water through Cobb Douglas production function, thereby to establish a tap-water supply-demand model under perfect competition market and government price control. Moreover, the study acts in concern with the maximum water supply limit to support the equilibrium and non-equilibrium pricing and quantity of tap water, consumer surplus, producer surplus, economic welfare and its loss or differences before and after the sediment removal of dams in Taiwan.
Before the sediment removal in 2010, the economic welfare in non-equilibrium was NT418.2 billion under government price control while the economic welfare loss was NT624.2 billion. Moreover, the economic welfare with maximum water supply limit was NT675.4 billion while the economic welfare loss was NT257.2 billion. Under perfect competition market, the economic welfare in non-equilibrium was NT433.5 billion while economic welfare loss was NT375 billion. Furthermore, the economic welfare under the maximum water supply limit was NT688.2 billion while the economic welfare loss was NT254.7 billion.
Before the sediment removal in 2010, the comparison with perfect competition market under government price control shows that the economic welfare in non-equilibrium reduced by NT15.3 billion and 3.53% in reduction. Moreover, the economic welfare with maximum water supply limit was NT12.8 billion and 1.86% in reduction while economic welfare difference reached surplus of NT2.5 billion and 1.77% increase. Furthermore, the economic welfare in equilibrium was increased by NT233.9 billion, an increase of 28.93% while the economic welfare loss was increased by NT249.2 billion, an increase of 66.45%.
After the sediment removal of one billion cubic meters in 2010, the economic welfare compared with non-removal of sediment in non-equilibrium under government price control increased to NT669.9 billion, an increase of 59.7% while the economic welfare loss was reduced to NT374.5 billion, a reduction of 40%. Moreover, the economic welfare remained with maximum water supply limit while the economic welfare difference was reduced to NT7.5 billion, a reduction of 97.08%. Under perfect competition market, the economic welfare in non-equilibrium increased to NT705 billion, an increase of 2.63% while the economic welfare in equilibrium increased to NT817.7 billion and an increase of 1.58% therefore the economic welfare loss was reduced to NT112.7 billion, a reduction of 69.95%. Furthermore, the economic welfare with maximum water supply limit increased to NT712.8 billion, an increase of 3.57% while the economic welfare difference was reduced to NT7.8 billion and a reduction of 96.94%.
After removing the sediment of one billion cubic meters in 2010, the economic welfare compared with perfect competition market in non-equilibrium under government price control was short of NT37.1 billion, a reduction of 5.55% while the economic welfare loss was increased by NT261.8 billion, an increase of 232.30%. Moreover, the economic welfare with maximum water supply limit was decreased by NT37.4 billion, a decrease of 5.25% while the economic welfare difference was reduced by NT0.3 billion, a decrease of 3.85%.
Before removing sediment in 2010, the economic welfare in non-equilibrium under government price control compared with that in equilibrium under perfect competition market was short of NT390.3 billion with a loss ratio of 77% which compared with sediment removal of one billion cubic meters were reduced to NT149.8 billion with a loss ratio reduced to 46%.
Before the sediment removal in 2010, the economic welfare in non-equilibrium with maximum water supply limit under government price control compared with that under perfect completion market with maximum water supply limit was short of NT270 billion with a difference ratio of 37%. The ratio compared with sediment removal of one billion cubic meters dropped to NT44.9 billion with a difference ratio reduced to 6%.
After removing one cubic meters of sediment in 2010, the existing water price under the government price control rose to NT20 per cubic meter while the economic welfare loss decreased from NT374.5 billion to NT197.2 billion compared with the price before the rise and the loss ratio dropped from 36% to 24%. Moreover, the economic welfare difference with maximum water supply limit dropped from NT7.5 billion to NT6.4 billion while the difference ratio declined from 6% to 1.014%.
Simply put, regardless of sediment removal increasing or existing water price rising under government price control and the increase in sediment removal under perfect competition market both reduced economic welfare loss or difference.

並列關鍵字

dam ； sediment removal ； tap water ； water market ； water price ； elasticity product function ； demand function ； supply function ； consumer surplus ； producer surplus ； economic welfare ； economic welfare loss

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