Principles of Economics for Scientists

Ga naar: navigatie, zoeken


Formularium met zowat alle gebruikte formules (2018-2019): Media:PoEfS_Formularium.pdf

Samenvatting vna de twee delen (2015-2016) on ShareLaTeX Oplossingen van de oefeningen uit Cabral's handboek kunnen op zijn website gevonden worden, de belangrijkste staan hier



Part 1

Question 1

Same as question 1 in the 2017-2018 exam (with different values)

Question 2

A consumer can spend their budget on X and Y for the prices px and py. The price of good X doubles.

Graphically show how the consumer's reaction to this increase can be split into an income and a substitution effect.

The amount of good X has to be on the X axis. All goods are normal goods. Also describe the role of the budget line.

Question 3

You have the following production function.

X = a * ln(L) + b * ln(K)

W = price of labour

r = price of capital

p = price of a good

  1. State the profit function and find the profit maximising quantity of capital and labour
  2. Derive the supply of the firm and its profit as a function of: p, W, and r
  3. What happens to the firm's output if capital + labour become very small

Question 4

Monopolist with 2 markets, A and B.

x_a = 20 - p_a

x_b = 30 - 2 * p_b

MC = 1

Calculate x* and p* on each market when the monopolist can price discriminate.

Question 5

Assume a perfectly competetive market.

x_d = a - b * p x_s = c * p

  1. Solve for x* and p*
  2. Find thie CS and pi of producer as functions of a, b, c

Hint (not mentioned in the exam itself) => pi = CS in perfect competition

Part 2

The startup Enigma has created a new software and is granted a patent which it wants to auction.

Demand function: p = 10 - q

MC reduces from 7 to 6 because of the innovation

Question 1

How much would a monopolist be willing to pay (per period of time) to acquire the innovation.

Question 2

Assume a Bertrand oligopoly with n >= 2 firms. The firms compete in price.

All firms have the same MC of 7. One firm will have a MC of 6 when they acquire the patent of the innovation.

How much would a firm in this system be willing te pay.

Question 3

Assume a Cournot duopoly with a MC = 7.

  1. Compute the pre-innovation price and profit per period of time for each firm
  2. Compute the price and per period profit of both firms if one of the firms is granted the patent
  3. How much is any of the duopolists willing to pay to acquire the innovation

Question 4

Assume a monopoly threatened by entry. Entry is not profitable at MC = 7 but it is at MC = 6.

If another firm enters the market the new system becomes a Cournot duopoly with MC_1 = 7 and MC_2 = 6.

  1. How much is the incumbent firm willing to pay for this innovation?
  2. How much is the entrant firm willing to pay for this innovation?
  3. If the innovation goes to the highest bidder, what is the influence of innovation on the market structure

Question 5

  1. Rank the various market structures by their incentive to innovate and explain
  2. Do you think that this ranking is specific to this example or more likely to be general
  3. Do you think that it is good that Enigma managed to get this patent


The questions should be 100% complete and are usable as a practice exam.

Part 1

Question 1

Demand + supply

Assume a perfectlty competetive market.

Demand curve is Xd = 120 - 2p

Supply curve is Xs = 2p - 20

  1. Draw the supply & demand curves in a diagram and clearly label the intersections
    1. What is the equilibrium quantity
    2. What is the equilibrium price
  2. How is the price elasticity of demand defined?
    1. Calculate price elasticity of the demand at the equilibrium price
  3. The government introduces a sales tax
    1. tax = 2 per unit sold, tax needs to be paid by consumers
    2. calculate the new p_eq and x_eq including taxes
  4. Now suppose that the tax is levied on the producers instead of the consumers
    1. Is there a difference from a welfare point of view in this model? Explain and prove your answer.

Question 2

  1. Suppose the total production cost of a firm operating in a perfectly competetive market is given by TC(X) and market price = p.
    1. Formally state the profit maximisation problem of the firm and derive the first order condition for profit maximisation
  2. output x according to x = K^0.5 * L^0.6 (production function)
    1. Is it characterised by decreasing, constant, or increasing return to scale?
    2. Explain what this implies for the relationship between inputs & outputs (i.e. if the quantity of input doubles, what happens to the output)
  3. First order condition yields L/K = 6/5 * r/w
    1. Derive the optimal demand for capital K as a function of the production level x and the function prices and the factor prices K*(x,w,r)

Question 3

p(x) = 200 - 2x constant MC = 10

  1. Calculate optimal price + quantity of monopolist
  2. Repeat the exercise but assume a perfectly competetive market
  3. Caluclate the welfare loss due to market power (calculate + compare welfare between 1 and 2)

Question 4

Utility maximising consumer U(x,y) = x^1/3 * Y^2/3

Budget B, Px and Py for goods x and y

  1. Specify at least 2 bundles of goods that lie on the indifference curve with U = 4 + sketch this curve and bundles
  2. Formally state the utility maximisation problem of the consumer and derive the 1st order functions that characterise the optimal consumption bundle (hint: use the lagrange function)
  3. Solve for this optimal consumption bundle

Part 2

A company developed something new and turned in a patent at the EPO

There will be a public auction for this patent and the license will go to the highest bidder.

The global goal of this exercise is to discover which system (monopoly, oligopoly, competitive market) renders the highest bidder.

Demand p = 120 -q

The innovation reduces the constant marginal cost of production from 90 to 80

  1. Confirm that
    1. This is a nondrastic innovation
    2. The marginal cost would have to be reduced to less than 15 for the innovation to be drastic
  2. Assume a monopoly
    1. How much is the firm willing to pay (per period of time) to acquire the innovation?
  3. Assume a Bertrand oligopoly. Calculate how much the latter firm is willing to pay for the innovation.
    1. n firms (n is >= 2) that compete in price
    2. before innovation, all firms have a MC of 90
    3. after innovation, one firm has a lower MC of 80
  4. Assume Cournot duopolists, identical MC of 90 before the innovation
    1. Confirm that the pre innovation price is 100, and that each firm has a profit per period of 100
    2. Suppose that one of firms is granted use for the innovation. Confirm that the price falls to 76,67 and compute the per period profit
    3. How much is any of these duopolists willing to pay to acquire the innovation
  5. Suppose that the industry is a monopoly threatened by entry. Production with MC = 90 does not make entry profitable but MC = 80 does. Incumbent firm can preclude entry by by buying the patent (remains monopolist with MC = 80). If monopolist does not acquire the innovation another firm can enter the market. When this happens the market structure becomes an assymetric Cournot duopoly with the MC of the incumbent firm = 90 and the MC of the entrant firm = 80.
    1. How much is the incumbent firm willing to pay for the innovation?
    2. How much is the entrant willing to pay for the innovation?
    3. If the innovation goes to the highest bidder, what is the influence of innovation on the market structure? Discuss this.
  6. Summary
    1. Rank the various market structures according to the incentivesto innovate that they convey to firms + comment on each ranking
    2. Is the ranking specific to this example or more likely to be general

Bonus question: Do you think that it is good that the EPO granted a patent for this innovation?


Both parts count for 50% of the final score each. The questions about part II didn't come from the document with possible exam questions this time.

Part 1

  1. Given the demand and supply for labour, find the equilibrium if employers pay 25% tax on the gross wage and employees pay 50% of their wage in taxes. Calculate the wedge created by taxes.
  2. Given marginal cost and an inverse demand function, calculate the equilibria under monopoly and perfect competition. Calculate the wellfare loss due to monopoly.
  3. I can't remember this one rn
  4. There's two technologies, A and B. Tomorow, one of them becomes the standard and the other will be obsolete. They both give a utility of 80 per period if they're the standard, or 0 if they're obsolete. They have an infinite lifespan and the interest rate is 10%. Technology A costs 250 and has 66% chance of becoming standard. Technology B costs 150 and has 34% chance of becoming standard. Which one has the highest expected utility today?

Part 2

  1. A new technology is invented that will lower the marginal cost of beer production from 70 to 60. The inverse demand for beer is p = 100 - q. The inventor of the technology has acquired a patent and will license the sole rights to the technology to the highest bidder.
    1. Calculate the willingness to pay of a sole monopolist.
    2. Calculate the willingness to pay of a firm in a Bertrand oligopoly with n players.
    3. Cournot duopoly: You're given the price and total quantities sold before the technology is licensed (MC = 70 for both firms) and after the license is sold (MC = 70 for firm 1 and 60 for firm 2), show that these are correct, calculate the profit of both firms and the willingness to pay of both firms.
    4. Incumbent versus entrant: A monopolist is threatened by a new entrant. The entrant will only enter the market if they get the license. Calculate the willingness to pay for both the monopolist and the entrant. Discuss the impact of this technology on the market structure if the license goes to the highest bidder.
    5. Now you've solved the previous questions, which market structure gives the highest incentive to pay for the license? Make a ranking, and give comments. Is this result specific to this situation or likely to be general?
  2. Bonus question: Now you know the impact of the patent in the previous question, do you think it's a good thing that the creator was able to acquire a patent? Elaborate your answer.


All questions about Part II (Question 3-6) came from the document with possible exam questions as posted on Toledo.

  1. Monopolist vs perfect competition. Calculate equilibria. Q = 300 - 3P. MC = 15
  2. (Utility) U(D,F) = DF. D being days on holiday domestically. F being days on holiday in a foreign country. Eric has a budget of 8000. Price of D is 160. Price of F 200. Calculate optimal utility. How many D vs F?
    1. Price of D becomes 250. Budget is x. Calculate D and F in function of x.
      • What budget x should Eric have to have the same utility as before?
      • Calculate D and F with that budget.
    2. Using your previous answers, discuss the effect of income and substitution.
  3. (NPV and PDV) Start a playground in an old industrial building costs 200000, lifetime benefits are 700000. However, there’s a 20 percent chance that the city board decides to change the purpose of the place where the industrial building is located on. Interest rate of 10%.
    • What’s the net present value?
    • What’s the net present value today, if you wait a year when the decision about the location is made by the city.
  4. Two firms compete (a la Cournot) in the cement market. Demand for cement is given by Q = 450 − 2 P. Firm 1’s marginal cost is constant at 50, firm 2’s at 40. A technological innovation allows firms to reduce marginal cost by 6.
    1. How much would each firm be willing to pay for the innovation if it were the only competitor to acquire it?
    2. Suppose the innovation costs 600. Consider a “metagame” where firms first simultaneously decide whether to acquire the innovation and then compete a la Cournot with whatever marginal cost results from the first stage.
      • What is the equilibrium of the 2x2 game played by firms at the technology choice stage?
  5. The Bertrand model of price competition suggests that, under a given set of conditions, firms make zero economic profits even if there are only two firms. However, there are many instances of industries with a small number of competitors where firms appear to earn more than zero economic profits.
    • Give an example of an industry dominated by a couple of firms where profits are significant.
    • Explain why the predictions of the Bertrand model are not borne out.
  6. Suppose that Ericsson and Nokia are the two primary competitors in the market for 4G handsets. Each firm must decide between two possible price levels: $100 and $90. Production cost is $40 per handset. Firm demand is as follows: if both firms price at 100, then Nokia sells 500 and Ericsson 800; if both firms price at 90, then sales are 800 and 900, respectively; if Nokia prices at 100 and Ericsson at 90, then Nokia’s sales drop to 400, whereas Ericsson’s increase to 1100; finally, if Nokia prices at 90 and Ericsson at 100 then Nokia sells 900 and Ericsson 700.
    • Suppose firms choose prices simultaneously. Describe the game and solve it.
    • Suppose that Ericsson has a limited capacity of 800k units per quarter. Moreover, all of the demand unfulfilled by Ericsson is transferred to Nokia. How would the analysis change?
    • Suppose you work for Nokia. Your Chief Intelligence Officer (CIO) is unsure whether Ericsson is capacity constrained or not. How much would you value this piece of info?

Under construction.