# Assignment

Question 1

Andrea has a budget of £21 to spend on toothbrushes and tooth paste. He does not receive any utility from owning a toothbrush, but for the consumption of every tube of tooth paste he gains a utility of 2 utils – but only if he owns a tooth brush. Without a tooth brush, Andrea gains no utility from consuming tooth paste. In addition, after consuming 10 tubes of tooth paste, a toothbrush needs to be replaced, i.e., Andrea needs to buy a new one. The current price of tooth brushes on the market is £5 and the current price for tooth paste is £1 per tube. Assume that Andrea aims to maximise consumer surplus.

• In a graph, draw total utility as a function of number of toothpaste tubes, assuming that Andrea buys 1 tooth brush.

(6 marks)

• How many tubes will Andrea buy if he wants to maximise consumer surplus, assuming that Andrea can buy any amount of tooth brushes? What is Andrea’s total consumer surplus?

(4 marks)

• How many tubes will he buy if the current price is £0.50 per tube?

(4 marks)

• Find Andrea’s income-consumption curve for tooth paste tubes for incomes between £0 and £21, assuming a price of £1 per tube.

(6 marks)

Question 2

1. Describe the relationship between elasticity and total revenue when considering an increase in price.

(6 marks)

You are the manager of a train company. Recently total sales have been a bit low and you are now considering means to give sales a boost. Market research has shown that currently the price of train tickets is historically low. Market research has also shown that the demand curve for train tickets is downward sloping. You may assume that your company is not a price taker on the market.

1. One of your colleagues has suggested that it is important to lower the price of train tickets. In that case, she argues, the demand will increase. Do you agree with her? Explain why.

(6 marks)

• She continues her argument by concluding that if the demand goes up, the total value of sales of train tickets should therefore increase. Do you agree with her? Explain why.

(8 marks)

Question 3

Consider a market where demand and supply satisfy the following equations

QD = 12 – 2 P,

QS = 2P.

1. Find the current equilibrium price and quantity.

(4 marks)

1. What is the total producer surplus if the market is in equilibrium?

(4 marks)

The government is considering a minimum price policy to increase producer surplus.

1. Explain by means of graphs how the introduction of a price floor can increase producer surplus.

(6 marks)

1. Find the (optimal) price floor that maximizes producer surplus.

(6 marks)

Question 4

Consider a duopoly market with 2 firms. Aggregate demand in this market is given by

Q = 500 – P,

where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B.

Assume the firms compete a la Cournot.

1. Find the inverse demand in this market.

(3 marks)

Note that marginal revenue for both firms is given by

MRA=500-2QA-QB,

MRB=500-QA-2QB.

1. Describe what a best-response curve is and how to find it. (5 marks)
• Derive the best-response function for each firm. (6 marks)
• What are the equilibrium quantities? (6 marks)
• What is the total quantity supplied on this market? (3 marks)
• What is the equilibrium price in this market? (3 marks)

Question 5

The following game is played by 2 players

 Adam Jack Left Middle Right Up 1,2 3,5 2,1 Middle 0,4 2,1 3,0 Down -1,1 4,3 0,2

• Determine all dominant strategies for Adam and Jack. (6 marks)
• Solve the equilibrium for this game. (8 marks)

END OF ASSESSMENT