📉 Economics 1 - Microeconomics

What the exam asks

107 questions across 10 topics, every one a calculation with freshly drawn numbers, graded within a small tolerance, with the worked path after you settle it.

• Opportunity Cost & Pareto Efficiency
• Comparative Advantage & Trade
• Consumer Theory
• Production & Cost Minimization
• Perfect Competition
• Market Equilibrium, Surplus & Taxes
• Monopoly
• Externalities & Pigouvian Taxes
• Price Ceilings & Floors
• Public Goods

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 · Opportunity Cost & Pareto Efficiency

   Jonas can spend Saturday evening in one of three ways: (i) attend a jazz concert (ticket 9.00 €; he would get there with the annual transit pass he bought last year for 35.00 €), (ii) play video games at home, which is worth a benefit of 9.00 € to him, or (iii) help a neighbor move furniture for a payment of 20.00 €, where the effort feels like a cost of 7.00 € to him. What is the minimum benefit the concert must provide so that Jonas chooses option (i)?

   Concert ticket

   9.00 €

   Transit pass, bought last year

   35.00 €

   Benefit of gaming

   9.00 €

   Moving job: pay / effort cost

   20.00 € / 7.00 €

   Answer: 22.00 €

   Solution: He picks the concert only if its surplus beats the best alternative: $b_{\text{concert}} - \text{expenditure} \geq \text{opportunity cost}$, where the opportunity cost is the highest surplus among the alternatives forgone. Gaming is worth 9.00 €; the moving job yields a producer surplus of 20.00 € − 7.00 € = 13.00 € - the best alternative. The transit pass is a sunk cost: it was paid for either way and never enters the decision. The concert must therefore be worth at least its expenditure plus the forgone surplus: 9.00 € + 13.00 € = 22.00 €.

2. Example 2 · Comparative Advantage & Trade

   Italy can produce 1,200 tons of wheat or 400 barrels of olive oil per year; Spain can produce 1,400 tons of wheat or 700 barrels of olive oil. They want to trade olive oil for wheat. What is the maximum price of one barrel of olive oil, measured in tons of wheat, at which both countries still gain from trade?

   Italy: wheat or olive oil

   1,200 or 400

   Spain: wheat or olive oil

   1,400 or 700

   Answer: 3.00

   Solution: Both gain only if the relative price lies between the two opportunity costs: $OC_{\text{Spain}} < p_{\text{olive oil}} < OC_{\text{Italy}}$. Opportunity cost of one barrel of olive oil: Italy 1,200 / 400 = 3 tons of wheat, Spain 1,400 / 700 = 2 tons of wheat. Spain (the low-cost producer) sells olive oil, and Italy will pay at most its own opportunity cost. The mutually beneficial range is 2 to 3 tons of wheat per barrel of olive oil, so the maximum price is 3.

3. Example 3 · Consumer Theory

   A student has Cobb-Douglas preferences $U(q_1, q_2) = q_1^{3/4} \cdot q_2^{1/4}$ over streaming hours ($q_1$) and cinema visits ($q_2$). Her budget is 256.00 €, one streaming hour costs 4.00 € and one cinema visit costs 3.00 €. How many streaming hours does she buy at the optimum?

   Budget m

   256.00 €

   Price $p_1$

   4.00 €

   Price $p_2$

   3.00 €

   Answer: 48.00 units

   Solution: With Cobb-Douglas utility $U = q_1^{a} q_2^{b}$ and $a + b = 1$, each exponent is the expenditure share: $q_1^* = a \cdot \frac{m}{p_1}$. Here $a = \frac{3}{4}$, so $q_1^*$ = 3/4 · 256.00 € / 4.00 € = 48 hours. (Analogously $q_2^* = \frac{1}{4} \cdot \frac{m}{p_2}$ = 21.33.)

4. Example 4 · Production & Cost Minimization

   A bottling plant with a fixed machine park produces $Q = -80 + 10 L - 0.05 L^2$ crates with labor input $L$. At which labor input does the average product of labor reach its maximum?

   Production function

   $Q = -80 + 10 L - 0.05 L^2$

   Answer: 40.00 units

   Solution: $AP_L = \frac{Q}{L} = -\frac{80}{L} + 10 - 0.05 L$; the maximum solves $\frac{dAP_L}{dL} = \frac{80}{L^2} - 0.05 = 0$, i.e. $L^* = \sqrt{80 / 0.05}$ = 40. At that point the marginal product $MP_L = 10 - 0.1 L$ equals the average product: both are 6 crates - the MP curve always crosses the AP curve exactly at its maximum (as long as $MP > AP$, one more worker pulls the average up).

5. Example 5 · Perfect Competition

   Firms in a competitive market all have the cost function $C(q) = 0.2 q^2 + 6 q + 20$, and entry and exit are free. What is the long-run break-even price?

   Cost function

   $C(q) = 0.2 q^2 + 6 q + 20$

   Answer: 10.00 €

   Solution: The long-run entry/exit threshold is the minimum of average cost: $AC(q) = 0.2 q + 6 + \frac{20}{q}$, minimized where $0.2 = \frac{20}{q^2}$, i.e. $q^* = \sqrt{F / 0.2}$ = 10. There $AC =$ 0.2 · 10 + 6 + 20/10 = 10.00 €. Above this price firms earn profit and entry occurs; below it they exit.

6. Example 6 · Market Equilibrium, Surplus & Taxes

   In the market for phone chargers, supply is $Q_S = 40 p - 40$ and demand is $Q_D = 410 - 50 p$. Compute the consumer surplus in the market equilibrium.

   Supply

   $Q_S = 40 p - 40$

   Demand

   $Q_D = 410 - 50 p$

   Answer: 256.00 €

   Solution: $CS = \frac{1}{2} \left( p_{max} - p^* \right) \cdot Q^*$, where $p_{max}$ is the demand choke price. Equilibrium: $p^* = \frac{410 + 40}{40 + 50}$ = 5.00 € with $Q^*$ = 160. Choke price: $p_{max} = \frac{410}{50}$ = 8.20. So CS = ½ · (8.20 − 5) · 160 = 256.00 €. (The producer surplus would be the triangle above the supply curve: ½ · (5 − 1) · 160 = 320.00 €.)

7. Example 7 · Monopoly

   A patent-holding pharma firm is the sole seller of a drug. Inverse demand is $P = 440 - 2 Q$, marginal cost is $MC = 1 Q + 200$, and fixed cost is 100.00 €. Which quantity maximizes its profit?

   Inverse demand

   $P = 440 - 2 Q$

   Marginal cost

   $MC = 1 Q + 200$

   Fixed cost

   100.00 €

   Answer: 48.00 units

   Solution: A monopolist produces where $MR = MC$, and with linear demand MR has twice the slope: $MR = 440 - 4 Q$. Setting $440 - 4 Q = 1 Q + 200$ gives $Q^* = \frac{440 - 200}{5}$ = 48 units. The fixed cost is irrelevant for the output choice - it shifts profit, not marginal profit.

8. Example 8 · Externalities & Pigouvian Taxes

   A gravel quarry sells at the fixed market price of 94.00 € per ton and has production costs $C(Q) = 1 Q^2$. Its dust damages a neighboring vineyard by 30.00 € for every ton. What is the socially optimal output of the quarry?

   Price per ton

   94.00 €

   Quarry costs

   $C(Q) = 1 Q^2$

   External damage per ton

   30.00 €

   Answer: 32.00 units

   Solution: The social optimum equates the price with the social marginal cost: $p = MC(Q) + MEC$, where $MEC$ is the marginal external cost borne by the vineyard. Here $94 = 2 Q + 30$ gives $Q_{soc}$ = 32 tons. Left alone, the quarry ignores the damage and produces where $p = MC$ only: $Q_{priv} = 94 / 2$ = 47.00 tons - more than is socially efficient, because part of its true cost falls on others.

9. Example 9 · Price Ceilings & Floors

   In Casablanca the daily market for gas cylinders has demand $Q_D = 480 - 30\,p$ and supply $Q_S = 30\,p$, where $p$ is the price in euros per cylinder. The regulator caps the price at 13.00 € per cylinder. What is the consumer surplus in this market with the cap in place?

   Demand

   $Q_D = 480 - 30\,p$

   Supply

   $Q_S = 30\,p$

   Price ceiling

   13.00 €

   Answer: 960.00 €

   Solution: $CS = \frac{1}{2} \left( \frac{A}{d} - p^* \right) Q^*$, the triangle between the demand curve and the price actually paid. Market clearing: $480 - 30\,p = 30\,p$ gives $p^*$ = 8.00 € and $Q^*$ = 240 cylinders. The ceiling of 13.00 € is above $p^*$, so it is not binding - price and quantity are the unregulated ones and the deadweight loss is zero. The choke price is $\frac{480}{30}$ = 16.00 €, so CS = ½ · (16 − 8) · 240 = 960.00 €.

10. Example 10 · Public Goods

    The 5 households of a village in Tuscany jointly fund the village fireworks show, a pure public good. Each household's marginal benefit from an extra minute of fireworks is $MB(Q) = 8 - Q$ euros, and the pyrotechnician charges a constant 15.00 € per minute. How many minutes of fireworks are socially efficient?

    Households

    5

    Marginal benefit per household

    $MB(Q) = 8 - Q$

    Marginal cost per minute

    15.00 €

    Answer: 5.00 units

    Solution: For a public good the Samuelson condition sums the marginal benefits vertically: $\sum_{i=1}^{m} MB_i(Q) = MC$, i.e. $m (a - Q) = c$, so $Q^E = a - \frac{c}{m}$. Here $5 \left( 8 - Q \right) = 15$ gives $Q^E = 8 - \frac{15}{5}$ = 5 minutes. At that level each household still values a further minute at 3.00 €, and 5 · 3.00 € = 15.00 € exactly covers the cost of one more minute.

Survival notes

• Everything is a curve, and the curve always shifts right after you have drawn it. Draw in pencil, price in ink.
• Deadweight loss is what happens to your weekend when you leave the surplus questions for Sunday night.
• A Pigouvian tax is the one tax the lecture wants you to like. Your first payslip will have opinions about the others.

Where it is studied

The first-semester rite of passage: lectures in the Audimax on Arcisstraße, tutorials wherever there was a free room, and the exam in Garching with a seating plan longer than the syllabus.

Arcisstraße: The main campus in the middle of München: the Audimax, the courtyard, and the ten-minute walk from the U-Bahn during which most of the lecture is forgotten again.

The whole BWL München map →