112 年 國立臺灣大學財務金融研究所丙組《經濟學原理》

1. 某廠商生產一種產品。其有兩個工廠可生產該產品。工廠一的生產函數為：$Q_1 = 12 \sqrt{L_1} K_1$，其中 $Q_1$ 為工廠一的產量，$L_1$ 與 $K_1$ 分別為工廠一勞動與資本的雇用量。工廠二的生產函數為：$Q_2 = 3 L_2 + 6 K_2$，其中 $Q_2$ 為工廠二的產量，$L_2$ 與 $K_2$ 分別為工廠二勞動與資本的雇用量。勞動的單位價格為 $w=1$，資本的單位價格為 $r=3$。若該廠商生產 381 單位的產品，其總成本為 (1)。若該廠商生產 576 單位的產品，其總成本為 (2)。

2. 某廠商為某產品的獨佔廠商,其面臨的需求曲線為: $P=336-3Q$,其中 $P$ 為產品價格, $Q$ 為需求量。該廠商有三個工廠可生產該產品。工廠一的總成本函數為: $C_1(q_1) = 6q_1^2$,其中 $q_1$ 為工廠一的產量。工廠二的總成本函數為: $C_2(q_2) = 3q_2^2$,其中 $q_2$ 為工廠二的產量。工廠三的總成本函數為: $C_3(q_3) = 2q_3^2$,其中 $q_3$ 為工廠三的產量。該廠商的最適產量為 (3)。當產量為最適產量時,產品價格為 (4),廠商利潤為 (5)。

3. 考慮如下的賽局。某產業中有兩家廠商,廠商決策變數為其產量。市場需求函數為: $P=68-0.5(q_1+q_2)$,其中 $P$ 為產品價格, $q_1$ 與 $q_2$ 分別為廠商一與二的產量。對每一家廠商來說,若進入市場,則總成本為: $TC(q) = 6 q+ 288$,其中 $q$ 為該廠商的產量;若不進入市場,則產量與總成本均為0。假設廠商只有在其利潤嚴格大於0時才進入市場,利潤小於或等於0則不進入。賽局進行順序如下。(i)廠商一決定是否進入市場;若進入市場則決定 $q_1$。(ii)廠商二觀察到廠商一的決策(是否進入市場與進入市場時的 $q_1$)後決定是否進入市場;若進入市場則決定 $q_2$。(iii)廠商利潤實現,賽局結束。
   (a) 若廠商一決定讓廠商二進入市場,則對廠商一來說最適的 $q_1$ 為 (6)。
   (b) 若廠商一決定讓廠商二不進入市場,則對廠商一來說最適的 $q_1$ 為 (7)。
   (c) 均衡時廠商一的利潤為 (8)。

4. 兩兄弟共同繼承一個父親過世後所遺留的工廠。此工廠對哥哥來說價值為 720 萬元,對弟弟來說價值為 $V$。兩兄弟均知工廠對哥哥的價值。弟弟知道 $V$ 確實的值為多少。哥哥不知道 $V$ 確實的值;對哥哥來說, $V$ 為隨機變數且其分配為介於 0 與 1,200 萬元之間的均等分配 (Uniform distribution)。分配規則如下。哥哥提出一價格 $P$ (單位萬元)。給定 $P$ 值,弟弟有兩種選擇:
   (i) 給哥哥 $0.5P$, 並取得工廠所有權。此時哥哥的報酬為: $0.5P$, 弟弟的報酬為: $V-0.5P$。
   (ii) 放棄工廠所有權, 並向哥哥收取 $0.5P$。此時哥哥的報酬為: $720-0.5P$, 弟弟的報酬為: $0.5P$。
   兄弟兩人均為風險中立,且均極大化自己的期望報酬。上述設定為此賽局的 Common knowledge。在此規則下,對哥哥最適的 $P$ 值為 (9)。就事前來看,哥哥取得工廠的機率為 (10)。

5. 某人有一子一女,均消費 $X$ 與 $Y$ 兩種財貨。女兒的效用函數為: $U_1(x_1, y_1) = 4 \ln x_1 + \ln y_1$,其中 $x_1$ 與 $y_1$ 分別為女兒消費 $X$ 與 $Y$ 的數量, $\ln$ 為自然對數。兒子的效用函數為: $U_2(x_2, y_2) = \min(x_2, 2 y_2\}$,其中 $x_2$ 與 $y_2$ 分別為兒子消費 $X$ 與 $Y$ 的數量, $\min$ 為極小值函數,是指大括號內所有數值中的最小值。某人要將 8 單位的 $X$ 與 4 單位的 $Y$ 分給女兒與兒子,其目標為極大化女兒與兒子兩人效用的總和。某人應分女兒 (11) 單位的 $X$,應分給兒子 (12) 單位的 $Y$。

6. 請閱讀以下 2023年1月 CNBC 的新聞報導後回答問題。
   Employers added 223,000 jobs in December, signaling a healthy job market Payroll growth decelerated in December but was still better than expected, a sign that the labor market remains strong even as the Federal Reserve tries to slow economic growth. Nonfarm payrolls increased by 223,000 for the month, above the Dow Jones estimate for 200,000, while the unemployment rate fell to 3.5%, 0.2 percentage point below the expectation. The job growth marked a small decrease from the 256,000 gain in November, which was revised down 7,000 from the initial estimate.

[此處有圖表，請對照原卷]
Monthly job creation in the U.S.
January through December 2022

Wage growth was less than expected in an indication that inflation pressures could be weakening. Average hourly earnings rose 0.3% for the month and increased 4.6% from a year ago. The respective estimates were for growth of 0.4% and 5%. By sector, leisure and hospitality led with 67,000 added jobs, followed by health care (55,000), construction (28,000) and social assistance (20,000). Stock market futures rallied following the release as investors look for signs that the jobs picture is cooling and taking inflation lower as well.
"From the market's perspective, the main thing they're responding to is the softer average hourly earnings number," said Drew Matus, chief market strategist at MetLife Investment Management. "People are turning this into a one-trick pony, and that one trick is whether this is inflationary or not inflationary. The unemployment rate doesn't matter much if average hourly earnings continue to soften."
The relative strength in job growth comes despite repeated efforts by the Fed to slow the economy, the labor market in particular. The central bank raised its benchmark interest rate seven times in 2022 for a total of 4.25 percentage points, with more increases likely on the way. Primarily, the Fed is looking to bridge a gap between demand and supply. As of November, there were about 1.7 job openings for every available worker, an imbalance that has held steady despite the Fed's rate hikes. The strong demand has pushed wages higher, though they mostly haven't kept up with inflation. December's wage data, though, could provide some encouragement that the Fed's efforts are impacting demand.
"There's some indication that things are moving in the right direction. We're seeing the impact of the blunt tools of monetary policy take effect," said Mike Loewengart, head of model portfolio construction for Morgan Stanley's Global Investment Office. "I don't think this is going to sway the Fed from a few additional raises going forward, but it no doubt is encouraging to see a moderation in wages."

[此處有圖表，請對照原卷]
Year-over-year change in average hourly earnings for all employees on private, nonfarm payrolls in the U.S.

The drop in the unemployment rate came as the labor force participation rate edged higher to 62.3%, still a full percentage point below where it was in February 2020, the month before the Covid-19 pandemic hit. A more encompassing measure of unemployment that takes into account discouraged workers and those holding part-time jobs for economic reasons also declined, falling to 6.5%, its lowest-ever reading in a data set that goes back to 1994. The headline unemployment rate is tied for the lowest since 1969. The household count of employment, used to calculate the unemployment rate, showed a huge gain for the month, rising 717,000. Economists have been watching the household survey, which has generally been lagging the establishment count.
The U.S. heads into 2023 with most economists expecting at least a shallow recession, the result of Fed policy tightening aimed at tamping down inflation still running near its highest level since the early 1980s. However, the economy closed 2022 on a strong note, with GDP growth tracking at a 3.8% rate, according to the Atlanta Fed.
Fed officials at their last meeting noted that they are encouraged by the latest inflation readings but will need to see continued progress before they are convinced that inflation is coming down and they can ease up on rate hikes. As things stand, markets are largely expecting the Fed to increase rates another quarter-percentage point at its next meeting, which concludes Feb. 1.

以下何者符合文章中關於 2022 年 12 月美國勞動市場的敘述？(答案可能不只一項,完全答對才給分) (13)
(a) 非農就業人口數較 11 月時下降,但仍高於市場分析師預期
(b) 失業率下降,且較市場分析師預期更低
(c) 時薪年成長率較 11 月時趨緩,但仍高於市場分析師預期
(d) 勞動參與率上升,但仍低於 Covid-19 爆發的時期

文中提到市場分析師對於美國就業市場的若干預期,請問以下哪個敘述最能描述這些預期形成的背景與原因? (14)
(a) 聯準會提高利率,導致美國通貨膨脹率攀高,進而使得工資上升,同時失業率攀高
(b) 美國工資上升,導致通貨膨脹率攀高,因此聯準會提高利率,讓勞動供給增加,進而使得失業率下降,工資也下降
(c) 美國工資上升,因此聯準會提高利率,導致通貨膨脹率降低,進而使得勞動需求增加,導致失業率下降,工資也上升
(d) 美國通貨膨脹率攀高,聯準會提高利率,導致投資需求與勞動需求下降,最終將使得失業率上升與工資下降

此一就業數據公布後,美國股市大漲,根據文中投資專家的意見請問以下因素何者最能解釋? (15)
(a) 工資的變動趨勢
(b) 失業率的變動趨勢
(c) 非農就業人口的變動趨勢
(d) 勞動參與率的變動趨勢

7. 請閱讀以下 2022年11月高盛銀行(Goldman Sachs,文中簡稱 GS)發布的 2023年總體經濟展望中有關於中國大陸的部分後答題。
   Our 2023 China outlook is a story of two halves with slow growth in the first half followed by a more pronounced rebound in the second half as the economy reopens (Exhibit 17). We expect weak growth in Q4 and Q1 as the Zero Covid Policy (ZCP) likely stays in place during the winter. In fact, the recent sharp rise in cases led us to have a significantly below-consensus Q4 estimate of 1.2% annualized.

[此處有圖表，請對照原卷]
Exhibit 17: Weak Growth Through H1; Rebound in H2

Despite our April reopening baseline, we forecast Q2 growth of just 2% annualized on our assumption that reopening initially triggers an increase in infections that keeps caution high. Weak growth in East Asian economies such as South Korea, Taiwan, and Hong Kong during the first quarter of exiting ZCP also supports our soft Q2 forecast. In contrast, we look for a meaningful reopening growth boost in H2, which will likely extend into 2024. As ZCP is currently still subtracting about 4-5% from the level of GDP, we see substantial room for a cyclical rebound as immunity levels rise and most households learn to live with the virus. Although clearly above consensus, our Q3 and Q4 forecasts of 10% and 6% annualized are not spectacular relative to other international reopening experiences. This is because we expect a continued drag from Covid caution as well as other headwinds, some cyclical and some more structural. On the cyclical side, fiscal policy is set to tighten if the domestic economy rebounds, and China's pandemic-related export boom should fade as global demand for tech, housing, and Covid-related products slows further. On the structural side, we see the contraction of the property sector and US chip export restrictions as multi-year drags. We estimate that the ongoing slide of the property sector will subtract around -1½pp from growth next year as it continues to delever and face demographic headwinds.
We recently also estimated that the new US restrictions on exports of advanced chips (and the equipment and software to produce them) to China will subtract about 4pp from China growth next year and 1.7% from the 2026 level of GDP, assuming US policymakers are serious about implementation. This reflects reduced production in China of both chips and goods using advanced chips, such as smartphones and computers.
The relatively muted rebound in aggregate demand-coupled with the relatively limited rise in inflation during reopening in other Asian economies also drives our benign forecast for 2023 inflation and monetary policy. Specifically, we expect core CPI to pick up only slightly from 0.7% to 1.2% next year, and the policy rate to stay flat at just 2%. Although we do see a sharper reopening boost in 2023H2 and 2024H1 than other forecasters, our long-run China views remain structurally below consensus. We estimate that much of the slowdown in actual China growth in recent years corresponds to a slowdown in potential growth to only 4.2% in 2023. We estimate that trend growth will slow further to just above 3% over the next decade on weakness in both demographics and productivity, and the long slide in the property market.

圖表17的縱軸座標為 Percent change, quarter annual rate,請問 2023 年第 1 季的值最有可能是如何計算出來的? 假設年第 q 季的實質 GDP 為 $Y_{i,q}$ (16)
(a) $(Y_{2023,1} - Y_{2022,1})/Y_{2022,1} - 1$
(b) $(1 + (Y_{2023,1} - Y_{2022,4})/Y_{2022,4}) - 1$
(c) $((Y_{2023,1} - Y_{2022,1})/Y_{2022,1} - 1) \times 4$
(d) $(Y_{2023,1} + Y_{2022,4} + Y_{2022,3} + Y_{2022,2}) / (Y_{2022,1} + Y_{2021,4} + Y_{2021,3} + Y_{2021,2}) - 1$

關於疫情對於中國大陸經濟的影響,以下哪些符合高盛判斷?(答案可能不只一項,完全答對才給分) (17)
(a) 由於老年人口疫苗接種率偏低,預期當局到第 2 季才會解封,導致第 1 季 GDP 成長率偏低
(b) 解封後可能出現大規模的感染,導致第 2 季 GDP 成長率偏低
(c) 到了下半年大眾免疫力提高,同時習慣在疫情下的生活後,經濟將有顯著的反彈
(d) 解封後可能如同歐美國家出現通貨膨脹的問題

8. 請閱讀以下網路媒體報導後回答問題。2
   It's a weird time to be a foreign-exchange trader. In the first 10 months of the year, the U.S. Dollar Index (ticker: DXY), which tracks the greenback's moves against a basket of currencies, racked up a 16% gain, its best rally since 1985. The Federal Reserve raised interest rates by nearly 4 percentage points as it tackled the highest inflation since the early 1980s, lifting yields on Treasury debt.
   Other countries raised rates too, but those in the U.S. rose faster, giving investors reason to buy the buck to take advantage of the higher yields. Russia's invasion of Ukraine and the surge in energy prices it unleashed added to the dollar's appeal as a haven currency.
   November, though, had a different story to tell. The dollar dropped 4.94% through late Wednesday afternoon, as data indicating that inflation is moderating raised hope that the Fed might slow down in raising interest rates. The dollar index's decline was the worst since September 2010, when it fell 5.39%.
   Investors are likely questioning if the dollar has reached its peak and is heading lower, which would be welcome news for U.S. multinationals whose earnings on sales made overseas have been crimped by the currency's strength. The answer is nuanced: The dollar has room to go higher, but it isn't likely to hold whatever gains it makes, according to economists and currency strategists at UBS, BofA and others. "We do see some possibility of the dollar regaining ground in the near term," said Brian Rose, senior economist at UBS.
   Rose's reasoning hinges on falling oil prices: Futures on West Texas Intermediate crude oil, which peaked in March at $123.70, had dropped to$80.55 as of the close on Tuesday. Prices may bounce back, according to Rose, who reminded investors that Europe is still debating price limits for Russian oil exports. A rebound in oil would "hurt the market" and send investors away from riskier investments and back into the dollar, the economist said.
   BofA strategists led by David Hauner said in a recent research note that the firm sees room for the dollar to gain in the first quarter of 2023 before hitting its peak. That is because the global economy is still at risk of stagflation-a combination of slow growth and high inflation-forcing central banks worldwide to respond by raising interest rates.
   The dollar would get a lift to the extent that the Fed raises rates more than other central banks. The consensus view is that the Fed will raise rates more slowly at its Dec. 13-14 policy meeting, with a half percentage-point move compared with 0.75-point increases at the past four meetings, but some other central banks have also slowed the pace at which they are tightening.
   In any case, it likely will be hard to convince market participants that calm will soon return to the markets and on the geopolitical front. There is "a wide range of risks that could keep investors defensive, which would support the dollar," said Edward Moya, senior market analyst at broker OANDA.
   While near-term uncertainty will help the dollar, there is a wide understanding that the currency will weaken at some point in 2023. Hauner bets on a peak after the first quarter, in part because he sees a case for China shifting away from the zero-Covid 19 policy that has tripped up its economy. That should ease the supply-chain problems that are hurting companies, improving sentiment about the global economy and reducing the need to hold dollars as a haven currency.
   Vanguard's global head of rates Roger Hallam agrees. Along with the China factor, he sees the gap between how aggressive the Fed and other central banks have been in raising rates is likely to diminish, weakening the currency in 2023. "You are probably past the peak in policy divergence," he told Barron's.

At the end of the day, "it's inevitable that the dollar will give up its gains," Rose said, calling the currency overvalued. "It's hard to stay at this kind of level." Still, expect some near-term volatility.

● 美元指數(DXY index)的計算公式為:
$DXY = 50.14348112 \times EUR/USD^{-0.576} \times USD/JPY^{-0.136} \times GBP/USD^{-0.119} \times USD/CAD^{-0.091} \times USD/SEK^{-0.042} \times USD/CHF^{-0.036}$
其中 $EUR/USD$ 為歐元兌換美元的匯率, $USD/JPY$ 為美元兌換日圓的匯率, 其餘匯率項目依此類推。$GBP$ 為英鎊, $CAD$ 為加元, $SEK$ 為瑞典克朗, $CHF$ 為瑞士法郎。
請問在其他條件不變之下, 若 $EUR/USD$ 由 1.00 上升至 1.10, $USD/JPY$ 由 130 下跌至 117, 則 $DXY$ 的變動百分比為?(只需填數字不需要百分比符號) (19)

● 以下何者是文中提到可能使得 $DXY$ 走高的因素?(答案可能不只一項,完全答對才給分) (20)
(a) 全球經濟疲軟,各國央行(包括美國)將繼續同幅升息
(b) 原油價格上漲
(c) 中國從疫情中解封
(d) 地緣政治的緊張關係

● 文中提到專家對於未來 $DXY$ 走勢的預測為 (21)
(a) 短期將走高, 中長期會有回檔
(b) 短期將走低, 中長期會反彈
(c) 持續走高
(d) 多空因素交錯, 將在區間盤整

9. 請參考以下網路文章的資訊回答問題。3
   The Federal Reserve's assets peaked most recently at $8.92 trillion on March 30, 2022. As of Jun. 2, 2022, they included$8.5 trillion in securities held outright. U.S. Treasury securities, mostly notes and bonds, accounted for $5.77 trillion of the total. The Fed also held mortgage-backed securities (MBS) worth$2.71 trillion. The Fed added assets worth approximately $2.8 trillion in the aftermath of the 2007-2008 financial crisis. The COVID-19 pandemic and the resulting financial panic impaired credit markets to such an extent that the Fed was forced to buy more than$100 billion in securities on a daily basis during the worst days in March 2020. The Fed eventually settled on a pace of $120 billion in monthly purchases, comprising$80 billion in Treasury debt and $40 billion in MBS. It increased its balance sheet by a total of$4.6 trillion in two years through March 2022.
   The Fed began reducing the pace of its securities purchases in November 2021 and brought them to a close in March 2022. In May 2022 the Fed's Federal Open Market Committee (FOMC) said the Fed would reduce its holdings by $30 billion in Treasury securities and$17.5 billion in agency debt and agency MBS monthly starting in June, and by $60 billion in Treasury securities and$35 billion in agency debt and MBS monthly from September 2022. That faster rate of balance sheet reduction would put the Fed on pace to shrink its assets by $1.14 trillion annually. The FOMC said balance sheet reduction would continue until the point, otherwise unspecified, at which the balance sheet is just large enough to efficiently implement monetary policy, primarily by continuing to target the federal funds rate.
   In a previous statement on the principles of balance sheet reduction, issued in January 2022, the FOMC said the fed funds rate remains its primary monetary policy tool, and said it planned to reduce its balance sheet primarily by adjusting the amounts reinvested from maturing securities. That means the Fed plans to continue buying Treasury debt and MBS, just not as fast as the securities it now holds mature and are redeemed. The FOMC also said it plans to hold primarily Treasury securities in the long run, "thereby minimizing the effect of Federal Reserve holdings on the allocation of credit across sectors of the economy." The statement implied the Fed plans to eliminate its holdings of MBS over time. The Fed's MBS purchases starting in 2020 helped to drive down mortgage rates, boosting housing demand, even as materials shortages and other market inefficiencies constrained supply.
   The shrinking of the Fed's balance sheet should be viewed as a victory, since only improvement in the economy's prospects is likely to bring it about. Because the Fed controls the U.S. currency, its balance sheet is practically limited only by the availability of assets and the Fed's preference for not usurping markets' role in setting securities prices and allocating economic resources. By shrinking the balance sheet, the Fed runs the risk of reversing some of the benefits accrued by its expansion. But if the economy is truly on the mend, it's likely to weather gradual change in the Fed's securities portfolio.

● 請問以下那些科目會出現在聯邦準備銀行資產負債表的資產中?(答案可能不只一項,完全答對才給分) (22)
(a) 流通在外美元
(b) 聯邦準備銀行發行給金融機構的定存單
(c) 美國政府國庫券與公債
(d) 不動產抵押貸款證券
(e) 逆回購協議

● 以下敘述何者正確?(答案可能不只一項,完全答對才給分) (23)
(a) 聯準會可以透過調高聯邦資金利率(升息)或是縮減資產負債表(縮表)來達到減少貨幣供給的目的,後者效果較前者溫和
(b) 聯準會縮表的方式包含對於部分或全部其持有且到期的公債或是不動產抵押貸款證券所返還的本金不再繼續購買新債(停止再投資),或是賣出尚未到期的公債或是不動產抵押貸款證券。2022年所採取的手段是前者
(c) 停止再投資公債將使得公債的需求減少,價格下降,殖利率上升,此舉將提高政府發行新債的成本
(d) 停止再投資不動產抵押貸款證券將使得該證券的殖利率上升,此舉將提高新承做不動產抵押貸款的利率,使得房市降溫

10. 請參考以下 2022年11月摩根大通銀行(J. P. Morgan)發布的 2023年投資展望中有關於新興市場投資機會的資訊回答問題。
    Emerging market equities had another very challenging year and disappointed investors' expectations for this promising high growth asset class. By the end of October, the MSCI Emerging Markets Index had lost 29% in 2022, underperforming developed market equities by 10%. Emerging markets were hit by multiple headwinds, including a sharply slowing global economy, escalating political risks, China's zero-Covid policy and the fastest Federal Reserve (Fed) tightening cycle in more than three decades.

Due to the sharp drop in share prices, equity valuations have fallen across the board. As a result, emerging market equities now look increasingly attractive from a valuation perspective. Our proprietary valuation composite for emerging markets, which includes price-to-earnings, price-to-book and price-to-cash flow ratios, as well as dividend yield, is currently significantly below its long-term average and is also cheap relative to global equities (Exhibit 15).

[此處有圖表，請對照原卷]
Exhibit 15: Emerging market valuations are increasingly attractive

請問以下敘述何者與文章提供的資訊最一致? (24)
(a) 相較於全球市場與新興市場,在相同的公司基本面表現之下,台灣上市公司的股價是較低的
(b) 相較於全球市場與新興市場,在相同的股價之下,台灣上市公司的股利是較低的
(c) 相較於全球市場與新興市場,在相同的公司基本面表現之下,台灣上市公司的股價報酬率是較低的
(d) 相較於全球市場與新興市場,在相同的股價之下,台灣上市公司的盈餘是較低的

11. 請問以下關於我國 101 年至今總體經濟指標的敘述何者正確?(答案可能不只一項,完全答對才給分) (25)
    (a) 年失業率都未超過 5%(因 111 年數據尚未公布所以不需考慮該年)
    (b) 年經濟成長率都未超過 5%(因 111 年數據尚未公布所以不需考慮該年)
    (c) 消費者物價指數年增率都未超過 2%(因 111 年數據尚未公布所以不需考慮該年)
    (d) 央行重貼現率都未超過 2%
    (e) 美元兌換新台幣的匯率都未高於 32

11. 請問以下關於我國 101 年至今總體經濟指標的敘述何者正確?(答案可能不只一項,完全答對才給分) (25)
    (a) 年失業率都未超過 5%(因 111 年數據尚未公布所以不需考慮該年)
    (b) 年經濟成長率都未超過 5%(因 111 年數據尚未公布所以不需考慮該年)
    (c) 消費者物價指數年增率都未超過 2%(因 111 年數據尚未公布所以不需考慮該年)
    (d) 央行重貼現率都未超過 2%
    (e) 美元兌換新台幣的匯率都未高於 32