ECON 3430 UQ Managerial Economics Questions

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Economics

ECON 3430

The University of Queensland Australia

ECON

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ECON3430: MANAGERIAL ECONOMICS Problem Set 1 (15%) Due: Monday, April 5th, 2021 at 4pm. Questions For all questions, make (and state) your own assumptions if a good answer requires additional information. 1) Jim is a salesperson at the DM paper company. The utility function of Jim is given by u(w, b, e) = w + b − c(e) where w ∈ ℝ is Jim′ s weekly wage, b is a bonus payment that is conditional on sales revenue, and c(e) is Jim′s cost of effort where c(e) = 1 if e < 10 and 1 c(e) = ( × (e − 10)2 ) if e ≥ 10. 2 Michael is Jim’s boss, who is maximising DM’s profits which are given by: π(w, b, e) = R(e) − w − b, where R(e) is the firm′ s sales revenues and R(e) = 100e Michael cannot observe Jim’s effort (e) directly but observes R(e) and can set the bonus level dependent on sales revenues. a. If Michael sets w=100 and b=0, what would be Jim’s effort level (e) and DM’s profits? (1 mark) b. If Michael sets w=0 and b=1000 conditional on reaching a sales target of 𝑅(𝑒) = 5000, what would be Jim’s effort level (e) and DM’s profits? (1 mark) c. If Michael sets w=100 and a bonus payment of 20% of sales revenues (i.e. 𝑏 = 0.2 × 𝑅(𝑒)) what would be Jim’s effort level (e) and DM’s profits? (1 mark) d. What is the optimal wage (w) and bonus payment (b) as a percentage of sales revenues that maximises DM’s profits? (1 mark) i. Briefly discuss the potential challenges with implementing such an employment contract in a real-world setting. (1 mark) e. Dwight is Jim’s partner. Michael assigns Jim and Dwight to work on a joint project, which can be described as a simultaneous move game with the following payoffs: Jim Work Hard Dwight Shirk Sabotage Work Hard 10, 12 10,20 -20, 15 Shirk 20, -5 0,0 25, -15 Sabotage 8, -30 -15, 30 -10, -10 Find the Nash equilibrium of this game. (1.5 marks) 2) Imagine your washing machine is broken, and you want to buy a brand new one. a) Search online and make a (random) list with ten washing machine models. (1 mark) b) What are the attributes of a washing machine that are most important to you? Describe your utility function u(a, b, c, d, p) where a, b, c, d are different attributes of the washing machine and p is the price. (1.5 marks) c) Make a choice using the “satisficing” heuristic. Describe your choice process. (1.5 marks) 3) Imagine you are the prime minister of Australia managing the response to the Covid-19 pandemic. Suppose your objective is to fully open Australian borders to international travel by January 1st, 2022. a. Write down 3 Key Results to measure your progress towards this objective. (1.5 marks) b. On the 27th of March, 2021, what was the number of COVID-19 vaccine doses administered per 100 people in Australia? (0.5 marks) c. Choose an OECD country (apart from Australia). Imagine that Australians use the number of COVID-19 vaccine doses administered per 100 people in your chosen OECD country as their reference point (𝑅𝑃). Suppose the difference between the number of COVID-19 vaccine doses administered per 100 people in Australia (AU) and Australians’ reference point (𝑅𝑃) determine Australians’ value 𝑣(𝑥), where (𝑥 = AU- RP). Assume that the Australian public’s value function is 𝑣(𝑥) = 300𝑥 𝑓𝑜𝑟 𝑙𝑜𝑠𝑠𝑒𝑠 (𝑥 < 0) 𝑎𝑛𝑑 𝑣(𝑥) = 100𝑥 𝑓𝑜𝑟 𝑔𝑎𝑖𝑛𝑠 (𝑥 ≥ 0) What was Australians’ value on the 1st of March 2021? (1 mark) d. What was Australians’ value on the 15th of March 2021? (1 mark) e. Comparing your citizens’ values for c) and d) above, would you say you did well in progressing the vaccine rollout in March? (0.5 marks) 2
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1
ECON3430: MANAGERIAL ECONOMICS
Problem Set 1 (15%) Due: Monday, April 5th, 2021 at 4pm.
Questions
For all questions, make (and state) your own assumptions if a good answer requires additional
information.
1) Jim is a salesperson at the DM paper company. The utility function of Jim is given by
u(w, b, e) = w + b − c(e) where w ∈ ℝ is Jim′ s weekly wage, b is a bonus payment that is
conditional on sales revenue, and c(e) is Jim′s cost of effort where c(e) = 1 if e < 10 and c(e) = (
12 × (e − 10) 2) if e ≥ 10.
Michael is Jim’s boss, who is maximising DM’s profits which are given by: π (w, b, e) = R(e) −
w − b, where R(e) is the firm′s sales revenues and R(e) = 100e Michael cannot observe Jim’s
effort (e) directly but observes R(e) and can set the bonus level dependent on sales revenues.
a. If Michael sets w=100 and b=0, what would be Jim’s effort level (e) and DM’s
profits? (1 mark)
Solution
Jim’s effort level
Bonus, b depends on sales revenue, R (e)
Assumption: b is directly proportional to R (e)
Therefore, if b = 0, R (e) = 0
Since R (e) = 100e
0 = 100e
Thus, Jim’s effort level, e = 0
DM’s profits, π
π (w, b, e) = R(e) − w – b
π =...


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