🏛️ Economics 2 - Macroeconomics

What the exam asks

90 questions across 12 topics, every one a calculation with freshly drawn numbers, graded within a small tolerance, with the worked path after you settle it.

• GDP Accounting & Value Added
• Growth Rates & GDP per Capita
• Real vs. Nominal GDP, Deflator & CPI
• Inflation & Real Interest Rates
• Goods Market & Fiscal Policy
• Efficiency Wages & Employment Rents
• Labour Market Statistics
• Intertemporal Choice
• Technology Choice & R&D
• Exchange Rates
• Money, Banks & Credit
• Solow Growth Model

Worked examples

One solved posting per topic, with the full calculation. In the trainer the same postings come back with fresh numbers every run, so memorising these answers buys you nothing - the method is the point.

1. Example 1 · GDP Accounting & Value Added

   The economy of Tuscany has exactly three producers. An olive grower imports fertilizer for 10,000.00 € and sells her entire olive harvest to the oil mill for 40,000.00 €; she pays 6,000.00 € in wages. The oil mill additionally imports glass bottles for 5,000.00 € and sells bottled olive oil worth 110,000.00 € - 50 % of it to the pesto factory, the rest directly to households; it pays 6,000.00 € in wages and 3,000.00 € in capital costs. The pesto factory turns the oil it bought into jars of pesto sold for 155,000.00 €, half of them exported. What is Tuscany's GDP?

   Grower: imported fertilizer

   10,000.00 €

   Grower: sales to oil mill

   40,000.00 €

   Mill: imported glass bottles

   5,000.00 €

   Mill: total sales

   110,000.00 €

   Share of oil mill output sold to pesto factory

   50 %

   Pesto factory: sales

   155,000.00 €

   Answer: 195,000.00 €

   Solution: $GDP = \sum_i VA_i = \sum_i \left( \text{sales}_i - \text{intermediate inputs}_i \right)$ - imported inputs are subtracted at the stage that buys them, and wages or capital costs only distribute the value added, they never enter the sum. Grower: 40,000.00 € − 10,000.00 € = 30,000.00 €. Mill: 110,000.00 € − 40,000.00 € − 5,000.00 € = 65,000.00 €. Pesto factory: it bought 50 % of the oil mill's output, i.e. 55,000.00 €, so 155,000.00 € − 55,000.00 € = 100,000.00 €. GDP = 195,000.00 €. Whether output goes to households, downstream firms or exports does not change any firm's value added.

2. Example 2 · Growth Rates & GDP per Capita

   Suppose real GDP of Spain grows at a constant rate of 2 % per year for 4 consecutive years. By what total percentage is GDP higher at the end of the 4 years than at the start?

   Annual growth rate g

   2 %

   Number of years T

   4

   Answer: 8.24 %

   Solution: $\left(1 + g\right)^T - 1$ - constant growth compounds: $1.02^{4} - 1$ = 8.24 %. Simply multiplying 2 % by 4 gives 8 % and understates the true change, because each year's growth also applies to the previous years' gains.

3. Example 3 · Real vs. Nominal GDP, Deflator & CPI

   The economy of Tuscany produces only bread and olive oil. In year 1 (the base year) it produces 410 loaves at 3.00 € each and 393 liters at 10.00 € each; in year 2 it produces 538 loaves at 4.00 € each and 419 liters at 13.00 € each. What is the growth rate of real GDP from year 1 to year 2?

   Bread year 1

   410 loaves at 3.00 €

   Olive oil year 1

   393 liters at 10.00 €

   Bread year 2

   538 loaves at 4.00 €

   Olive oil year 2

   419 liters at 13.00 €

   Base year

   year 1

   Answer: 12.48 %

   Solution: $g^{real} = \frac{\sum p^{base} \, q_2}{\sum p^{base} \, q_1} - 1$ - value both years' quantities at base-year prices, so only quantity changes count. Year 1: 5,160.00 €. Year 2 at year-1 prices: 3.00 € · 538 + 10.00 € · 419 = 5,804.00 €. Growth: 5,804.00 € / 5,160.00 € − 1 = 12.48 %. The year-2 prices are only needed for nominal GDP, not here.

4. Example 4 · Inflation & Real Interest Rates

   Mateus lends 700.00 € to a friend in Brazil for one year and receives a repayment of 735.00 €. Over that year, inflation turns out to be 1.6 %. What real interest rate did Mateus earn (Fisher approximation)?

   Amount lent

   700.00 €

   Repayment after one year

   735.00 €

   Inflation

   1.6 %

   Answer: 3.40 %

   Solution: $r = i - \pi$ - first recover the nominal rate from the repayment: $i = \frac{735}{700} - 1$ = 5 %. Then subtract inflation: 5 % − 1.6 % = 3.4 %. In real terms Mateus can buy 3.4 % more than a year ago, not 5 %.

5. Example 5 · Goods Market & Fiscal Policy

   Portugal has consumption $C = c_0 + c_1 (1 - t) Y$ with $c_0 = 100$, $c_1 = 0.5$ and an income tax rate of 20 %. Investment is 1,510, government purchases 525, exports 425, imports 400. What is consumption in the goods-market equilibrium?

   Autonomous consumption $c_0$

   100

   Marginal propensity to consume $c_1$

   0.5

   Income tax rate t

   20 %

   Investment I

   1,510

   Government purchases G

   525

   Exports X

   425

   Imports M

   400

   Answer: 1,540.00

   Solution: $C = c_0 + c_1 (1 - t) \cdot Y^*$ - first solve for equilibrium output, then feed it into the consumption function. $Y^* = \frac{c_0 + I + G + X - M}{1 - c_1(1-t)}$ = 2,160 / 0.6 = 3,600. Then C = 100 + 0.5 · 0.8 · 3,600 = 1,540.

6. Example 6 · Efficiency Wages & Employment Rents

   A fish factory in Hamburg observes that its workers' effort depends on the hourly wage $w$ (in €): $e(w) = 4\sqrt{w} - 4$. Output is proportional to effort. What efficiency wage does the firm set?

   Effort function

   $e(w) = 4\sqrt{w} - 4$

   Answer: 4.00 €

   Solution: $e'(w) \cdot w = e(w)$ - the Solow condition: at the efficiency wage, the elasticity of effort with respect to the wage is one. Here $\frac{4}{2\sqrt{w}} \cdot w = 4\sqrt{w} - 4$, so $\frac{4}{2}\sqrt{w} = 4$ and $\sqrt{w^*} = 2$, giving $w^*$ = 4.00 € with effort $e(w^*) = 4$.

7. Example 7 · Labour Market Statistics

   The Netherlands has a working-age population of 42 million, a participation rate of 66 % and an unemployment rate of 5 %. How many million people are employed?

   Working-age population

   42 million

   Participation rate

   66 %

   Unemployment rate

   5 %

   Answer: 26.33

   Solution: $E = WAP \cdot \text{participation rate} \cdot (1 - u)$ - the participation rate gives the labour force, and the unemployment rate carves out the jobless share of that labour force: 42 · 0.66 = 27.72 million in the labour force, times 0.95 = 26.33 million employed.

8. Example 8 · Intertemporal Choice

   Tobias faces an intertemporal budget line with intercepts 60 thousand € (consume everything this year) and 69 thousand € (consume everything next year). He decides to consume 20 thousand € this year. What is the maximum he can consume next year (in thousand €)?

   Maximum consumption this year

   60 thousand €

   Maximum consumption next year

   69 thousand €

   Chosen consumption this year

   20 thousand €

   Answer: 46.00

   Solution: $C_2 = C_2^{max} - (1 + r) \cdot C_1$ - every unit consumed today costs $1+r$ units of consumption tomorrow. The implied interest factor is 69 / 60 = 1.15, so $C_2$ = 69 − 1.15 · 20 = 46.00 thousand €.

9. Example 9 · Technology Choice & R&D

   A pizzeria in Naples can bake one batch of pizzas with technique A (8 units of gas, 1 worker-day) or technique B (3 units of gas, 3 worker-days). A worker-day costs 10.00 €. At the old gas price of 8.00 € per unit the firm correctly chose technique B. The gas price now falls to 3.00 € per unit while the wage stays put. What is the rent per batch from switching to technique A?

   Technique A

   8 gas + 1 worker-day

   Technique B

   3 gas + 3 worker-days

   Wage per worker-day

   10.00 €

   Old gas price

   8.00 €

   New gas price

   3.00 €

   Answer: 5.00 €

   Solution: $c_T = e_T \cdot p_{gas} + l_T \cdot w$ per technique, and the switching rent is the cost difference at the new prices. Old price: A costs 74.00 €, B costs 54.00 € - B was the right choice. New price: A costs 34.00 €, B costs 39.00 €. Switching to the gas-intensive technique A now saves 39.00 € − 34.00 € = 5.00 € per batch.

10. Example 10 · Exchange Rates

    The Danish krone (currency of Denmark) and the Polish zloty (currency of Poland) are both quoted against the euro: one euro costs 6.40 kroner, and one euro costs 2.82 zloty. What is the cross rate in kroner per Polish zloty?

    Kroner per euro

    6.40

    Zloty per euro

    2.82

    Answer: 2.27

    Solution: $E_{DKK/PLN} = \frac{E_{DKK/EUR}}{E_{PLN/EUR}}$ - both quotes share the euro, so dividing them cancels it: 6.40 / 2.82 = 2.27 kroner per Polish zloty. Multiplying instead of dividing, or flipping the ratio, are the classic traps.

11. Example 11 · Money, Banks & Credit

    A bank in Italy has total assets of 600 billion € and a net worth of 23 billion €. By what percentage would the value of its assets have to fall to wipe out the bank's net worth entirely?

    Total assets

    600 billion €

    Net worth (equity)

    23 billion €

    Answer: 3.83 %

    Solution: $\frac{\text{net worth}}{\text{assets}} \cdot 100$ - liabilities are fixed, so every euro of asset losses eats a euro of equity; equity is gone when losses reach the full net worth: 23 / 600 = 3.83 %. This is the flip side of leverage: the higher the leverage, the smaller the asset fall a bank can survive.

12. Example 12 · Solow Growth Model

    A Solow economy has production per effective worker $f(k) = \sqrt{k}$. The savings rate is 10 %, population grows at 0 %, technology at 1 %, and capital depreciates at 4 %. What is the steady-state capital stock per effective worker $k^*$?

    Production per effective worker

    $f(k) = \sqrt{k}$

    Savings rate s

    10 %

    Population growth n

    0 %

    Technological progress g

    1 %

    Depreciation rate δ

    4 %

    Answer: 4.00

    Solution: $s \cdot f(k^*) = (n + g + \delta) \cdot k^*$ - in the steady state, saving per effective worker exactly covers the capital dilution. With $f(k) = \sqrt{k}$: $s \sqrt{k^*} = (n+g+\delta) k^*$, so $\sqrt{k^*} = \frac{s}{n+g+\delta}$ = 10 % / 5 % = 2, giving $k^*$ = 4.

Survival notes

• Real versus nominal is the whole course. If a number went up and nobody is happier, deflate it.
• The Solow model has a steady state. Your study plan does not. One of these is examinable.
• The fiscal multiplier explains why one round of drinks in the Mensa becomes four. Aggregate demand, empirically confirmed.

Where it is studied

Second semester, same Audimax, larger numbers. The GDP you compute in the exam is bigger than Ottobrunn's, Straubing's and Heilbronn's combined, and it still has to add up.

Straubing: The campus on the Danube. Fewer people, same formulas, better air. The BroDollars count exactly the same there.

The whole BWL München map →