4. Suppose that South Africa is trying to find the efficient amount of coal to extract, which is a depletable resource. There are two periods and the inverse demand function is P = 15 - 0.5QD and the marginal cost of extraction is 5.

(a.) Use the static efficiency model to find the efficient allocation for the first time period. Also, compute the price of coal at that efficient allocation.

(b.) Now suppose that the total available quantity of coal is Q = 40. Is the static efficiency criteria sufficient? If yes, what is the efficient allocation of coal over the two periods? If no, why not?

(c.) Now suppose that the total available quantity of coal is Q = 35. Is the static efficiency criteria sufficient? If yes, what is the efficient allocation of coal over the two periods? If no, why not?

answer

watching

106

views

For unlimited access to Homework Help, a Homework+ subscription is required.

You have 0 free answers left.
Get unlimited access to 3.8 million step-by-step answers.

Get unlimited access

Already have an account? Log in

Nestor RutherfordLv2

2 Feb 2019

Unlock all answers

Get 1 free homework help answer.

Already have an account? Log in

Related questions

Instructions: Please answer the following questions related to current (Period 1) and future (Period 2) demands for groundwater within the context of our two-period model.

Suppose that Period 1 demand for groundwater is given by the linear equation QUOTE PToday=$10-0.4*Q Today. Furthermore, suppose climate change causes Period 2: demand for groundwater to be different linear equations, QUOTE PFuture=$12-0.3*Q future. The current reserves of groundwater to be allocated across both periods is Q=Q1+Q2=16, and future demand is discounted at a rate of so that the present value of future demand is given by 11.08*P2 and the present value of future net benefits is 11.08*NB2. The marginal cost of extraction is constant and equal in both periods: MC1=MC2=$3.

a) Determine the optimal quantity of groundwater to extract in Periods 1 and 2 when users in both periods are considered in one problem. Is more extracted today or in the future, and why? What does the marginal user cost?

b) Determine the number of units extracted in Periods 1 and 2 if current Period 1 user lack secure property rights over the aquifer. That is, solve the problem as if Period 1 users considered only their consumption in their problem.

c) Explain in words/in graphs/in equations (as you prefer) why the quantities extracted in b) represent a loss of overall welfare/net benefits when compared to the extraction in a).

d) What would the discount rate need to be to optimally solve the two-period model with equal quantities extracted in both periods? That is, what r sets present value of demand or net benefits equal in both periods while maintaining equilibrium extraction quantities at Q1*=Q2*=8?

pinksea-lion365

2.) Consider a beekeeper that is deciding how much honey to produce. The beekeeper gains a benefit from producing honey, represented by the marginal benefit function and which is given by:

MB= 300 - 6Q

where Q is barrels of honey.

In addition, she has a marginal cost function, which reflects her cost of producing honey; this is given by:

MC= 40 + 4Q

The beekeeperâs total profit function is given by:

Profit= 360Q + Q^2

The more honey the beekeeper produces, the more bees there are to pollinate a neighboring apple orchard. Thus, in addition to the private benefit accruing to the beekeeper herself, there is also a marginal external benefit to the apple orchard, which is given by:

MEB= 100 - 2Q

And a total external benefit to the apple orchard given by:

TEB= 100Q - Q^2

a. Find an expression for the social marginal benefit (SMB) in this case, defined as you think appropriate. Calculate the level of honey production that will arise if the beekeeper acts in her self-interest only. Calculate the socially efficient level of honey production as well.

b. Suppose that the beekeeper and the owner of the apple orchard enter into negotiations. The orchard owner wants to offer a payment to the beekeeper to change honey production from her self-interested production level to the socially efficient level (all at once). What is the maximum total payment that the orchard owner would be willing to pay for this overall change? What is the minimum total payment that the beekeeper would require before making this overall change?

c. Assume that, if a deal is reached, each party must pay $35 in legal fees to finalize it. If there are no additional transaction costs, will the socially efficient quantity be reached? Explain.

d. Irrespective of your answer to part c, assume that the beekeeper and the orchard owner come to a private agreement to set honey production at the socially efficient quantity. However, now suppose that a policymaker reads somewhere that honey production provides a positive externality to apple orchards, and therefore decides that the beekeeper should be provided with a production subsidy for each unit of honey that the beekeeper is willing to produce. With this subsidy in place, the beekeeper decides to increase production by an additional 5 barrels. Calculate the associated efficiency loss.

e. If honey is good to eat and bees are good for trees, why is there such a thing as too much honey?

silvercrow642

Suppose you are the proprietor of the only bar in Dallas. Since you are the only place in town for people to get drinks you exercise some market power and face a downward sloping demand curve for drinks given by P = 10 - (3/2)Q for each individual. Your total costs are given by TC = Q. There are 100 individuals with identical demand.

Assuming that you must follow a uniform pricing strategy, what is the profit maximizing price and quantity and the associated profit? What is consumer surplus? Is the market efficient?
If each person is charged their reservation price, what type of price discrimination is this? Assuming you can engage in this pricing scheme, what is your profit maximizing price and quantity and the associated profit? What is consumer surplus? Is the market efficient?
Now assume that you decide to try a two-part tariff scheme instead, charging a price per drink and a cover charge at the door. What is the optimal two-part tariff charged to each person? How many drinks will be sold to each person? What is your total profit associated with this scheme? What is the total consumer surplus? Is the market efficient?
Assume that your clientele is composed of two types: 50 customers are heavy drinkers with individual demand described by P_H = 15 - Q_H and 50 customers are light drinkers with individual demand described by P_L = 10 -3Q_L. Which group would you rather charge a higher price? Why?
Assume that the market is split as described before. There is no constraint on the number of drinks you can sell. You can charge a different price to each group. What is the optimal price and corresponding quantity for each segment of the market? What is your total profit under this scheme? What type of price discrimination is this?
Assume that the market is split as described before. The city of Dallas tells you that can only sell 325 drinks in total. You can charge a different price to each group. What is the optimal price and corresponding quantity for each segment of the market? What is your total profit under this scheme?