## Economics-AW-Q309 Online Services

**Assignment 2**

There are 3 questions worth a total of 50 marks. Please answer all questions.

(20 marks)The demand for cargo bikes in New Zealand is Q^d=(5000-P)I/200 where I is average income in thousands (i.e. if average income is 50,000 I=50)

(8 marks) Suppose Avanti decides to begin producing cargo bikes, and there are currently no other companies supplying the New Zealand market. If their marginal cost is expected to be $500, what is the maximum level of fixed costs at which they would be willing to enter the market? [assume average income is $40,000]

Since, she is the only producer, we know that Avanti will produce at a point where MR = MC.

At I = 40, we get the following demand curve, P = 5000 – 5Qd

So MR = MC point gives, Q = 450. And P = $ 2750

Let F be the fixed costs.

So profits = P*Q – (F+MC*Q), and this must be greater than 0.

So, (2750-500)*450 – F > 0

Which gives: F< $ 1,012,500
So, Fixed costs must be less than this value.
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(8 marks) Now suppose fixed costs are 500,000, and if a second firm enters they will compete with Avanti through Cournot competition. Find the Cournot equilibrium and determine whether a second firm will choose to enter. .

Profit functions for each firm

πi = (P*qi) – (F + cqi)

= (5000 – 5(qi + qj)) – (500,000 + 500*qi)

The best response function for firm i using the FOCs:

Qi(qj) = {4500-5qj)/10

Solving the two best response functions simultaneously, we get q1 = q2 = 300

So we get P = 2000

We can see that at such prices and quantity, the profits are negative due to the high fixed costs.

So the second firm will not enter.

(4 marks) Explain using a graph how an increase in average income (market size) might encourage more firms to enter the market.

We can see it by using the following diagram:

As income increases, the demand increases, so an average firm gets more for its quantity that it is selling currently. As a result, other firms see this and find it profitable to enter in the market.

(15 marks) The market for BanhMi in Auckland CBD consists of 6restaurants operating in monopolistic competition. Suppose that these firms face monthly fixed costs of $5,000 and marginal costs of $3.

Draw the average cost and marginal cost curves for a representative firm. (5 marks)

Total cost = 5000 + 3Q

AC = 5000/Q + 3

MC = 3

So, we have the following graph.

If the short run market price is $6 and each firm sells 2000 units per month, what will occur in the long run? Explain and show on a graph. (5 marks)

We will have the following graph

When P = 6, and Q = 2000,

We can see that AC = 5.5.

Since P>AC, there will be positive profits in the market. As a result new firms will enter into the market in the long run.

Suppose that BanhMi become more popular as a lunch option, and market demand increases. Explain the short run and long run effects on the market, including price, firm-level quantity and number of firms. Use graphs to explain your answer. (5 marks).

In the short run, with increase in demand, the price will increase to P1. In the long run, firms will see it as opportunity of positive profits, and new firms will enter along with a rise in the quantity in the number of firms, till the long run price becomes equal to 3, which is the MC.

(15 marks) Suppose Audrey and Nicky are cousins with a destructive streak. Audrey is 1 year old and has a 10% chance of creating substantial damage in the next year, in which case the expected cost is $2000. Nicky is 2 years old and has a 5% chance of creating substantial damage in the next year, in which case the expected cost is $3000.In both cases their parents would be responsible for the damage, and their parents are risk averse

(6 marks) If the insurance company were able to differentiate based on age, and offered actuarially fair insurance, how much would they charge Audrey’s parents and Nicky’s parents for insurance?

Actuarially fair insurance premium is exactly equal to the loss multiplied by its probability of happening.

For Audrey, it will be 0.1*2000 = $200

For Nicky, it will be 0.05*3000 = $150

(4 marks) Once Nicky’s parents have bought insurance, how is their behavior likely to change compared with when they did not have insurance? What is this called?.

They will be less caring towards avoiding the destruction caused by Nicky when they have bought the insurance. This is the problem of moral Hazard.

(5 marks) Suppose Nicky’s parents have $10,000 of wealth initially, but their wealth increases to $20,000 due to a bequest. Find the effect of this change in initial wealth on their maximum willingness to pay for insurance if their utility function is U(c)=√c where c is their total wealth.

Initially their expected wealth is = 0.95*10,000 + 0.05*7,000 = $9,850, which gives them a utility of 99.247.

Now, their expected wealth is = 0.95*20,000 + 0.05*17,000 = $19,850, giving them an expected utility of 140.89.

Since their expected utility has increased they will be willing to pay more, with the bequests.

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