,ECS4862 Assignment 2 (COMPLETE ANSWERS)
2025 - DUE 17 June 2025
MULTIPLE CHOICE,ASSURED EXCELLENCE
QUESTION 1
(a) Suppose there are only two firms in a fast-moving consumer
goods market. The producer is deciding whether to sell high-
quality or low-quality products. The purchaser has two options
either to buy or not buy. The annual profits associated with
each strategy are given in the table below:
Producer
Sell high-quality goods
Sell low-quality goods
Purchaser
Buy
200 ; 160
340 ; 80
Not buy
160 ; 280
240 ; 200
,i) Determine whether either player has a dominant strategy.
Explain. (4)
ii) Determine whether there is a Nash equilibrium in this game.
If so, what is it? If not, explain. (4)
iii) Explain the concept of prisoner dilemma in game theory. Is
this game an example of the prisoners’ dilemma? Explain. (5)
iv) Assuming a sequential-move game in which the Purchaser
chooses the strategy first, determine the pure Nash equilibrium
of this game. (4)
b) Siphiwe is in between jobs and has two job offers. She
approaches you to get an economist's advice. Her first job offer
pays a salary of R40 000 without a bonus. The second job offers
a base salary of R20 000 but offers the possibility of a R40 000
bonus on top of your base salary. Siphiwe believes that there is
a one-half chance of earning the bonus. In addition, she tells
you her utility function is given by 𝑈𝑈(𝑌𝑌)=2𝑌𝑌+10√𝑌𝑌where,
Y is income. In your advice,
i) Calculate the expected salary under each job offer (2)
ii) Determine which job offer Siphiwe should choose. (4)
iii) Using answers to b(i) and b(ii), determine Siphiwe's attitude
towards risk (2)
c) Suppose Adam has a utility function given by 𝑈𝑈(𝑌𝑌)=1−
10𝑌𝑌−2 where Y denotes the monetary payoff from an
, investment in a thousand rands. Adam is considering an
investment that will give him a payoff of R10 000 (thus, Y = 10)
with a probability of 0.6 and a payoff of R5 000 (Y = 5) with a
probability of 0.4. It will cost Adam R8 000 to invest.
(i) Is Adam risk-loving, risk averse or risk neutral? Explain why?
(5)
(ii) Should Adam invest? Why or why not? (5)
QUESTION 1
(a) Game Theory: Producer and Purchaser
We have a payoff matrix (Producer payoff ; Purchaser payoff):
Purchaser Buy Purchaser Not Buy
Producer Sell High-Quality 200 ; 160 160 ; 280
Producer Sell Low-Quality 340 ; 80 240 ; 200
(a)(i) Dominant Strategy
• Definition: A dominant strategy is one that yields a higher
payoff for a player no matter what the other player does.
Let's analyze each player:
2025 - DUE 17 June 2025
MULTIPLE CHOICE,ASSURED EXCELLENCE
QUESTION 1
(a) Suppose there are only two firms in a fast-moving consumer
goods market. The producer is deciding whether to sell high-
quality or low-quality products. The purchaser has two options
either to buy or not buy. The annual profits associated with
each strategy are given in the table below:
Producer
Sell high-quality goods
Sell low-quality goods
Purchaser
Buy
200 ; 160
340 ; 80
Not buy
160 ; 280
240 ; 200
,i) Determine whether either player has a dominant strategy.
Explain. (4)
ii) Determine whether there is a Nash equilibrium in this game.
If so, what is it? If not, explain. (4)
iii) Explain the concept of prisoner dilemma in game theory. Is
this game an example of the prisoners’ dilemma? Explain. (5)
iv) Assuming a sequential-move game in which the Purchaser
chooses the strategy first, determine the pure Nash equilibrium
of this game. (4)
b) Siphiwe is in between jobs and has two job offers. She
approaches you to get an economist's advice. Her first job offer
pays a salary of R40 000 without a bonus. The second job offers
a base salary of R20 000 but offers the possibility of a R40 000
bonus on top of your base salary. Siphiwe believes that there is
a one-half chance of earning the bonus. In addition, she tells
you her utility function is given by 𝑈𝑈(𝑌𝑌)=2𝑌𝑌+10√𝑌𝑌where,
Y is income. In your advice,
i) Calculate the expected salary under each job offer (2)
ii) Determine which job offer Siphiwe should choose. (4)
iii) Using answers to b(i) and b(ii), determine Siphiwe's attitude
towards risk (2)
c) Suppose Adam has a utility function given by 𝑈𝑈(𝑌𝑌)=1−
10𝑌𝑌−2 where Y denotes the monetary payoff from an
, investment in a thousand rands. Adam is considering an
investment that will give him a payoff of R10 000 (thus, Y = 10)
with a probability of 0.6 and a payoff of R5 000 (Y = 5) with a
probability of 0.4. It will cost Adam R8 000 to invest.
(i) Is Adam risk-loving, risk averse or risk neutral? Explain why?
(5)
(ii) Should Adam invest? Why or why not? (5)
QUESTION 1
(a) Game Theory: Producer and Purchaser
We have a payoff matrix (Producer payoff ; Purchaser payoff):
Purchaser Buy Purchaser Not Buy
Producer Sell High-Quality 200 ; 160 160 ; 280
Producer Sell Low-Quality 340 ; 80 240 ; 200
(a)(i) Dominant Strategy
• Definition: A dominant strategy is one that yields a higher
payoff for a player no matter what the other player does.
Let's analyze each player:
