Exam (elaborations)
Sample Paper for EC231
- Module
- EC231 (EC231)
- Institution
- The University Of Warwick (UoW)
This is the first sample paper for EC231 giving detailed responses for questions for section A
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1. The demand for a sugary food is represented by the demand function( , ) = 50 − 2 + 2√
where p is price and A measures the amount of advertising. The marginal cost of producing the
product is 20.
a) Assume that the cost of advertising is 5 per unit. What price should the firm set, and how
much advertising will it do? (10 marks)
The profit function is
( , ) = ( − 20) 50 − 2 + 2 −6
First-order conditions are
( , )
= 90 + 2 −2
( , ) − 20
= −6
√
Hence
40 + 2√ + 100
=
4
− 20
=
5
So
205 25
= = 22.8; = = 0.308
9 81
Now suppose that the government bans advertising for the product.
b) If everything else stays the same, what will be the firm’s optimal price and profit be? (8
marks)
Substituting A=0 in the above, we get
2 ∗ 20 + 100
= = 22.5
4
= 2.5 ∗ 5 = 12.5
c) Compare profits earned before and after the change in policy towards advertising to check
whether the firm is better off under the new policy. (4 marks)
Profits in part a are 13.89, so the firm is worse off under the advertising ban.
d) What if anything can we say about whether consumers are better or worse off after the
change in policy? (8 marks)
The ban leads to a 10-11% reduction in quantity and a 1.2% reduction in price. Elasticity is close
to -9, but cannot say for sure, esp. given health benefits of the substantial quantity reduction.
2. A cinema manager finds through experience that there are broadly two categories of film
shown, those that are a “success” (subscript s) and those that are a “failure” (subscript f). The
films are 75% success and 25% failure. From past records, the owner has estimated the demand
for each type of film as
= 150 − 0.1
= 180 − 0.4
respectively (p is price in pence and q is quantity). Subject to the cinema’s capacity of 300 not
being exceeded, the marginal cost per customer is zero, although there are of course significant
fixed costs of running the cinema.
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