UNIVERSITY OF STELLENBOSCH
DEPARTMENT OF ECONOMICS
ECONOMICS 214
ASSESSMENT A1: 19 MAY 2021
Time: 3 hours
Marks:
EXAMINORS:
Dr E Moses
INTERNAL MODERATOR:
Dr G du Rand
100
NO PROGRAMMABLE POCKET CALCULATORS ARE ALLOWED.
SHOW ALL CALCULATIONS.
QUESTION 1
Cassper consumes two goods, good X and good Y. Cassper's income is R200 per week and his
utility function is given by U (X,Y) = 2XY. The price of good X is R10, and the price of good
Y is R5.
What is Cassper’s total utility when he consumes his best affordable bundle of goods X and
Y? How much of product X and product Y does Cassper consume when he is consuming his
best affordable bundle?
[5]
QUESTION 2
Use indifference curve analysis to illustrate how the consumer’s demand curve can be derived.
Define all concepts used.
[5]
QUESTION 3
A market has 1000 identical consumers and the demand curve of each individual is represented
by the following demand curve function:
P = 12 – 3Qi
Where:
P = Price of the product in Rand
Qi = Quantity demanded in units by an individual
3.1
Write down a function for the market demand curve (also referred to as the price function
or inverse demand function).
[3]
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3.2
If the price of the product is currently R6 per unit, what is the price elasticity of demand
at this point on the market demand curve?
[3]
QUESTION 4
Due to a sudden increase in the oil price the Minister of Finance decides to introduce a fuel tax
of R5.00 per litre to discourage consumers from buying petrol. Before the tax, the typical
consumer earned R127 500 per annum and bought 1 200 litres at a price of R10 per litre. The
price elasticity of demand for petrol is -0.3 and the income elasticity of the demand for petrol
for the typical consumer is 0.5. What is the size of the tax rebate that the Minister must
introduce to fully compensate the consumer for the total fuel tax that will be paid? How many
litres of petrol will the consumer buy after the tax is imposed and the tax rebate is received?
Also comment on whether the Minister was successful in his aim to decrease the consumption
of petrol.
[9]
QUESTION 5
Suppose the demand for cinema tickets is given by Q = 200 000 – 2 000P.
5.1
If the price (P) is R50, how much will total revenue be?
[2]
5.2
What is the price elasticity of demand at this point?
[4]
QUESTION 6
With the aid of a graph, explain how wanting to own an exclusive product such as a luxury
watch could produce a negative network externality in the effect of price on quantity demanded.
[8]
QUESTION 7
A firm produces pink watches using two factories with the following marginal cost functions,
respectively: MC1 = 0.8Q1 and MC2 = 4 + 0.4Q2.
7.1
If the firm wants to minimise costs and produce 16 pink watches, how much should it
produce at each factory?
7.2
[4]
If the firm wants to minimise costs and produce 8 pink watches, how much should it
produce at each factory?
[2]
QUESTION 8
Explain why a perfectly competitive firm would shut down temporarily in the short run if the
market price is lower than the average variable cost of production.
[4]
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QUESTION 9
If the total cost function is 10Q3 - 50Q2 + 1000 Q + 500 at what output is the AVC = MC? [3]
QUESTION 10
Assume that Dogg Pound Ltd, a rap music company, operates in a perfectly competitive market
that is in long-run equilibrium. The industry is characterised by the fact that the average
production cost per rap song increases if more songs are produced. Explain, with the aid of
graphs, how the long-run supply curve of the industry is determined if the demand for rap songs
increases.
[7]
QUESTION 11
Are the following firms characterized by increasing, decreasing or constant returns to scale in
terms of production?
11.1
11.2
A firm has the production function Q = K0.5L0.3.
[1]
A firm currently produces 300 watches with 80 units of capital and 160 units of labour.
It doubles both its capital and labour and then produces 640 watches.
[2]
QUESTION 12
A firm produces output with the following production function:
Q(K, L) = K0.5L0.5
where K and L denote its capital and labour inputs, respectively. If the price of labour is R1
and the price of capital is R2, what quantities of capital and labour should it use to produce 40
units of output?
[6]
QUESTION 13
With the aid of a graph, explain how and why a monopolist firm would use price discrimination
to increase their total revenue in a market where one segment of buyers wants to buy the
product immediately when the product is launched, and the other segment of buyers is willing
to wait a bit before they buy.
[8]
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QUESTION 14
Two Puck is the only seller of masks in Stellenbosch. Its market demand curve is represented
by P = 320 – 2Q. Two Puck produces masks at a constant cost of R80 per mask. Answer the
questions that follow.
14.1
14.2
What is Two Puck's profit-maximising output level?
[2]
At what price will Two Puck sell its masks if it produces the profit-maximising
output?
[1]
14.3
Two Puck sells its entire company to two firms, Mad Masks and King Covers, each
acquiring half of the original company. The market demand for masks in Stellenbosch
14.3.1
14.3.2
is still given by P = 320 – 2Q and marginal cost MC = R80.
If this is a Cournot duopoly, how many masks will be sold by each firm and at what
prices?
[7]
If this was a Bertrand duopoly, how many masks would be sold by each firm and at
what prices? Explain the reason for this outcome.
[4]
QUESTION 15
With the aid of a graph, explain how price-setting is done in an oligopolistic market with one
dominant firm and a few smaller firms.
[10]
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