ACE 210 HW 1+2

Suppose there are two people: Anna and Bob. Anna's demand curve for donuts is P= 10 - Qa . Bob's demand curve is: P= 10 - 2Qb. What is the most efficient way to divide up 6 donuts between the two?

Anna gets: 4 donuts. Bob gets: 2 donuts. First, set the two marginal benefits equal: 10 - Qa = 10 - 2Qb → Qa = 2Qb Next, plug this into the quantity constraint: Q = Qa + Qb = 6 → 3Qb = 6 → Qb = 2 Finally, plug the value of Qb into the quantity constraint to get Qa: Qa + 2 = 6 → Qa = 4

Suppose Anna likes fireworks. Her marginal benefit from setting off fireworks is given by (Q is number of fireworks): MBa = 70 - Q She needs to buy the fireworks from Indiana. She needs to drive there and pay for the fireworks. Thus her marginal cost is: MCa = 10 + Q Bob wants to have a quiet evening after a long day at work. Anna's fireworks generate a marginal cost to him of: MCb = 10 + 3Q What is the market outcome? In other words, how many fireworks will Anna set off if she only takes her own costs and benefits into account? What is the socially optimal number of fireworks that Anna should set off if she takes into account Bob's costs?

At the market equilibrium, Anna only cares about her own costs and benefits: MBa = MCa --> 70 - Q = 10 + Q --> Qm=30 MBa=MCa+MCb --> 70-Q=20+4Q --> Q*=10

Suppose there are two people: Anna and Bob. Anna's demand curve for donuts is P= 10 - Qa . Bob's demand curve for donuts is: P= 10 - 2Qb. a) Derive their joint (aggregate) marginal benefit from donuts. b) Calculate total benefits from 15 donuts.

Their joint marginal benefit from donuts can be described by the function: MB = 10 - (2/3) Q Their total benefit from 15 donuts is 75. Derive the aggregate marginal benefit curve in the following way: P= 10 - Qa → Qa = 10 - P P= 10 - 2Qb → Qb = 5 - ½ P Q = Qa + Qb = 15 - (3/2)P → P = 10 - (2/3)Q The total benefit is the area of the triangle under the demand curve: ½ * 15 * 10 = 75.

Suppose two bakeries produce donuts. Firm A's supply curve is P = 20 + 2Qa. Firm B's supply curve is: P = 20 + Qb. a) Derive their joint supply curve. b) Calculate total cost of producing 30 donuts.

Their joint supply curve is: 20 + (2/3)Q Their total cost of producing 30 donuts is: 900 Derive the aggregate supply curve in the following way: P = 20 + 2Qa → Qa = (1/2)P - 10 P = 20 + Qb → Qb = P - 20 Q = Qa + Qb = (3/2)P - 30 → P = 20 + (2/3)Q Derive the total cost by calculating the area under the curve and to the left of 30. This is sum of the area of the triangle and the rectangle. The total area of the triangle under the supply curve is: ½ * 30 * 20 = 300. The area of the rectangle is: 30 * 20 = 600. So the area to the left of 30 is 600 + 300 = 900.

2. Which of the following statements about open‐access resources are true? a) Open‐access resources will tend to be under‐exploited relative to the social optimum. b) Open‐access resources will tend to be over‐exploited relative to the social optimum. c) Open‐access resources are public goods. d) Open access resources could result in the tragedy of the commons due to lack of clear property rights. e) Users maximize the economic value of an open‐access resource while hurting the environment.

b) Open‐access resources will tend to be over‐exploited relative to the social optimum. (X) c) Open‐access resources are public goods. d) Open access resources could result in the tragedy of the commons due to lack of clear property rights. (X)

When there is a positive externality in the market for a good, which of these statements is true? (choose all the correct answers) a) The private market tends to produce more than is socially efficient. b) The private market tends to produce less than is socially efficient. c) The social planner sets marginal social benefit equal to firms' marginal cost. d) Firms set their marginal private cost equal to the marginal external cost. e) Production of this good should be banned.

b) The private market tends to produce less than is socially efficient. (X) c) The social planner sets marginal social benefit equal to firms' marginal cost. (X)

Which of the following statements about a production possibility curve for a country are true? a.) anywhere outside the PPC is a possibility for production b.) PPCs are downward sloping - there is a tradeoff between the environment and goods c.) PPCs will always shift in for future generations d.) All points on the PPC give the same amount of production of the two goods.

b.) is true. PPCs generally move over time, but they can either shift out or in depending on whether things are going well for the country. Only the points inside or on the PPC are attainable. Different points on PPC give us different combinations of production of the two goods.