Find linear demand function and find elasticity of demand

Reference no: EM13860194

I just wanted to know if you can assist me with the completion of the given assignment.

Exercise D1: Can two preferences curves intersect? Why or why not?

Exercise D2: In a world with only two goods (A and B) and a typical consumer with total income of I, draw the demand function for good A in the following cases:

1. Good A and B are percieved as perfect complements;

2. U (Q_A; Q_B ) = 2Q_A + Q_B ;

How do these demand functions change if PB increases?

Exercise D3: A company wants to estimate the market demand for its new product A. It hires a bunch of consultants who come out with this information: the market demand is linear; if good A was to be sold for free (P=0), the company would sell 1000 units of it; for a price equal or higher than 100, however, the quantity sold would be 0. With this information:

1. Find the linear demand function for A (hint : start from the inverse linear demand)

2. Find the elasticity of the demand when P=50

3. Find the CS when P=50

4. Consultants are divided. Some suggest that the firm should price at 50, others suggest that 60 would be a better price. Somehow, the company trusts you more than anyone else. Assuming that the firm has no costs in producing good A (i.e. it just wants to maximize revenues), which price would you choose between the two?

Exercise E1: For each of the following cases, show in a supply-demand graph the new equilibrium, explaining carefully how and why curves move.

1. There is an increase in oil prices. (oil is used to produce goods).

2. Coinsurance is reduced.

3. Consumers become more price sensitive

Exercise E2: The demand for a market is P=500-5Q. The supply curve is P=100+3Q.

1. Find price and quantities in equilibrium.
2. Find the value of W=CS+SS
3. Now imagine that a fixed fee of 80 per unit sold is imposed in the market. Show the new situation in a graph.
4. Find the new equilibrium price(s) and quantities.
5. Calculate the deadweight loss from taxation (it is the area of a triangle)

Exercise MF1: One monopolistic firm faces a demand function of the form: P = 10 - Q. The related Marginal Revenues are represented by MR = 10 - 2Q. Marginal Costs are equal to 2, while total costs are C = 2Q.

1. Find the monopolistic profits.

2. Now consider the same case with 2 firms in the market (i.e. the value πM is the one found in point 1). As both firms produce the same good, the perfectly informed consumers always buy only the cheapest product between the two. Both firms have a discount rate of δ = 0.6. They both think they will stay in the market infinitely. In this setting, show formally that they can form a cartel. (hint : look at the slides...)

3. In this setting, how many firms do we need in order to make the cartel unsustainable?

Exercise MF2: Firms producing good A face a demand function of the form: P = 100 - 5Q. The MC is constant and equal to 10 for each firm in the market.

1. Find the quantity produced in the market if firms are price-taker.

2. The government in the country estimates that the pollution produced by the market for A impose a total cost on society equal to C = 20Q. The government concludes that A is over-provided. Explain with a graph why the government reaches this conclusion?

3. Find the SMC associated to the production of A. (hint : the SMC is the PMC + the MC of the externality)

4. Find the optimal quantity of A from a society point of view.

5. The government suggests to solve the problem by taxation. What type of tax should be imposed? How much would the tax need to be?

Exercise MF3: Two types of agents can buy an insurance: the L type and the H type. The L type is characterized by a probability of getting ill of πL = 0.1, while for the H type πL = 0.3. Half of the insurable population is of the L type and the other half is of the H type.

1. It can be shown that the optimal situation for the insurance firm is to set a premium per unit of reimbursement equal to the probability of the negative event. Can this policy be applied? What type of problems can arise in this context?

2. If the firm can not tell who is H and who is L, what premium will it offer (the firm behave as described in class)?

3. What type of contract can the firm offer so that consumers can self- select into the right risk group? (here you can only give an intuition, in words. We mentioned this in class.)

4. Can this type of contract solve the problem you identified in point 1? (Rotshild-Stiglitz as in the slides).

Reference no: EM13860194

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