☒
Quality assured
Copenhagen Business School
Department: Department of Economics
Name of study: BSc in Digital Management
Course name: Economics in the Digital Age
Exam type: Ordinary or re-take
Examination type: Written sit-in – 4 hours
File format at submission: PDF
Date and time: May 12, 2023 9:00-13:00
Directions:
•
•
•
•
•
This exam has 5 pages, including this page
This exam has 4 main questions, each with several sub questions. In total, there are
33 sub questions on the exam of varying difficulty.
On average, you should spend about 7 minutes per sub question, but again, there is
considerable variability in the difficulty of some questions. I have placed a very
approximate time guidance next to each main question accordingly.
If I ask you to provide one sentence of clarification, please provide one sentence (not
20)
Please show your work so that if you make a silly mistake, I can still verify that you
know what you are doing.
Question 1 : 40 minutes
Consider the market for generic digital stock photos in a perfectly competitive market. Let the demand curve
for the stock photo be represented by the equation QD = 1000 - 2p, where p is the price of the stock photo. The
supply curve in this perfectly competitive market is given by QS = 200 + 3p, where p is the price of the stock
photo.
a) Determine the equilibrium price and quantity or the stock photo in this market.
b) Calculate the price elasticity of demand for the stock photo at the equilibrium price.
c) Suppose the government imposes a per unit tax (t) of $10 on the supplier of the stock photo. Determine the
new equilibrium price and quantity after the tax is imposed. Calculate the share (percent) of the tax borne by
consumers.
d) Sketch the post-tax equilibrium above in a supply and demand diagram, label the areas on the diagram
corresponding to the consumer surplus, producer surplus and deadweight loss. If the government could waive
a magic wand that could simultaneously make both the supply and demand curve more elastic or more inelastic,
which would they choose and why (in one sentence)?
e) In a sentence, explain what the deadweight loss is.
f) By hiring a consulting firm promises the Association of Danish Photographers that they an successfully
pressure the government to impose the tax on consumers rather than on producers (but keeping the level of the
tax the same). How much should the Association be willing to pay the consultants to achieve this?
2
Question 2: 40 minutes
Consider a consumer, Mette, who consumes two goods: e-books (E) and bags of microwave popcorn (M).
Mette has a utility function given by U(E, M) = E0.6 * M0.4 + 100. Mette has allocated a 2000DKK budget to
the consumption of these two goods. Mette seeks to maximize her utility, subject to her budget constraint.
Assume the price of e-books (PE) is 120 DKK and the price of a bag of microwave popcorn (PM) is 40 DKK.
a) Derive Mette's optimal consumption levels for e-books and bags of microwave popcorn. Show your
calculations.
b) Derive the demand curve for e-books (E).
c) The price of E-books now drops to 100. Draw in a diagram the Mette’s original budget constraint, and
optimal consumption bundle, the new budget constraint and new optimal bundle. Illustrate in the diagram the
income effect and the substitution effect. Make sure to label all points clearly.
d) Another consumer, Anders, has the same budget, faces the same prices, but has a utility function of U(E,
M) = 10 * E0.6 * M0.4 + 200. Will Anders' consumption of e-books be larger than Mette's? Please justify your
answer with a one-sentence explanation.
e) Joe switches between only consuming popcorn or only consuming movies depending on price. Would the
utility equation above for Mette makes sense for Joe? What type of utility function might make more sense for
him?
f) Mette had a very lucky day! She won the lottery. As a consequence, she decided to increase her popcorn, ebook budget to 10,000 DKK. What is Mette’s new expenditure on popcorn? Hint: this should not take long
3
Question 3 100 minutes
The royalty-free digital music industry is a segment of the broader music industry that focuses on the creation,
distribution, and licensing of music tracks that can be used in various projects without the need to pay ongoing
royalties to the original creators. There are many music producers and composers creating royalty-free tracks,
and a large number of potential buyers such as video creators, marketers, and podcasters looking for
background music or audio assets for their projects. While musical tracks can be unique in style and genre, the
overall purpose and usage of royalty-free music are similar across the board. Buyers can often find multiple
suitable tracks for their needs, and the tracks are highly substitutable for one another. With relatively low
barriers to entry, new music creators can easily join the market by producing and selling their music on various
platforms, and they can also exit the market without significant losses. Due to the online nature of the market,
information about prices, licensing terms, and available tracks is easily accessible to all participants. This
transparency allows buyers to compare offerings and make informed decisions. Because of these characteristics
of the royalty-free digital music industry, using a perfectly competitive model can provide insight.
Consider n identical royalty-free music production firms, each with a Cobb-Douglas production function given
by q = L0.25 K0.25, where q is the quantity of music tracks produced by each firm, L is labor input and K is
capital input. Assume that the wage rate (w) is 200DKK and the cost of capital (r) is 50DKK. Also, assume
that the firms have fixed costs (FC) of 3,200DKK.
a) If a firm triples all factors of its production, what can we say about the resulting level of content
produced(q)?
b) Derive the marginal products of labor (MPL) and capital (MPK).
c) Does the production function exhibits diminishing marginal product of labor? Provide justification.
d) In the short run, what does your answer in c) imply about the relationship between q and marginal costs?
e) Derive the cost function, C(q), of a cost minimizing firm (Make sure this is a function of q only).
f) What is the long run market supply curve?
g) Given the market demand curve QD= 32,400 - 20P, find the price and quantity in the long run equilibrium.
Solve for the number of firms, n, operating in this equilibrium.
h) Do any of these firms have an incentive to lower their price relative to the market price? Do they have an
incentive to increase their market price? Explain in two sentences.
i) What is each firm’s short run marginal cost curve? And what is the short run market supply curve?
Assume that the introduction of an innovative, easy-to-use podcast production software leads to an increase
in royalty-free music demand such that at any price, there are 20,000 more units of royalty-free music
demanded (content providing firms are unaffected).
j) For each of the following elements of the short run equilibrium that results from the new demand, indicate
whether it has increased, decreased, or remained unchanged relative to the initial longrun equilibrium prior
to the demand shock (no need to calculate these explicitly): Price, firm output (q), profits earned by each
firm, and number of firms operating in the market.
k) Explain (in one sentence) how the market will reach a new long run equilibrium.
l) ChatGPT has just been introduced, changing each firm's production function to the following:
q = (ALL)0.25 (AKK) 0.25, where AL and AK are the productivity terms for labor and capital, respectively,
that depend on the adoption of ChatGPT. Discuss the conditions on AL and AK under which firms may
hire more workers in the short run but hire fewer workers in the long run (i.e., that ChatGPT is a laborsaving technology in the long run).
4
Question 4: 60 minutes
Consider a content creation firm that uses labor (L) and capital (K) as inputs in its production process. To
produce one “unit” of content, the firm requires 2 units of labor and 1 unit of capital. In other words, the firm's
production function is q = min(L, 2K). Assume that the wage rate (w) is 100DKK and the cost of capital (r) is
50DKK, and each firm has a fixed cost (FC) of 100,000DKK.
a) Derive the cost function in terms of q. Would few or many firms lead to lower total costs at the industry
level? Justify your answer in one sentence.
b) Assume only one firm operates in this industry and you have just taken over as CEO. Your predecessor
hired a consulting firm to estimate that the market demand curve, which they estimated to be:
QD = 8000 - 20P. What is the marginal revenue function?
c) In one or two sentences, explain why the marginal revenue curve is below the average revenue (demand)
in this case.
d) What is the profit maximizing price and quantity assuming that this demand is correct?
e) How much higher is this monopoly price than the welfare maximizing price?
f) Draw the market demand curve, firm marginal revenue curve, marginal cost, average total cost curves.
Label the welfare maximizing quantity, price, monopoly price, and monopoly quantity. Label the areas
corresponding to producer surplus (PS), consumer surplus (CS), and deadweight loss (DWL) associated
with the equilibrium in this market.
g) You’d like to run your own marketing analysis rather than relying on someone else’s team, so you have
your marketing department run some randomized control experiments to try and uncover your
consumers’ sensitivity to price. They estimate that consumer’s sensitivity to price is rather stable for
realistic value of q and is -2.0. How should you change the price your firm is charging to ensure you
are profit maximizing?
h) Reviewing your consumer base, you quickly realize two groups stand out: 1) individuals, who mainly
consume content for entertainment, and 2) businesses, who consume largely to learn about industry
trends and to gain insights into their target markets. These two types of customers are easy to verify
according to whether or not they have a CVR. You have your quantitative marketing team estimate
relevant elasticities for these two groups and finds that the elasticity of demand for the individuals is
-6 and for businesses it is -3. Given that the cost associated with providing content to both of these
consumer types is the same, what should the firm be charging each group?
i) As you are a graduate of a great program at CBS in digital management, you recognize profits are being
left on the table: most of your consumers are interacting with your business online. In fact, with the
rapidly growing power of predictive models and your ability to collect data on individuals, your
company will be getting very close to being able to exactly uncover individuals’ reservation prices. In
one sentence, explain how your ability to uncover individuals’ reservation prices will change the
marginal revenue function you found in part c) above. What are the implications on societal welfare as
a whole, for your profits, and for your consumers’ welfare (one sentence)?
5