Week 3

• A general equilibrium covers all consumers and firms
• A partial equilibrium uses just 1 consumer and 1 form who maximise utility and profit based on a given budget set
• we use a very simple set up with 1 organisation and 1 firm when we would ideally use all of them
• In consumer theory, consumers exchange their budget/position for a more optimal allocation
• In an exchange economy, there are N agents, summed to i, and L goods, summed to j
• We simplify the exchange economy to 2 people (agents) and 2 goods
• The gradient of an indifference curve is the MRS
• Society involves all the consumers involved in the model
• An edgeworth box represents the total endowment of each good
• In an edgeworth box, one consumer starts in the bottom left, and the other starts from the top right, so both their endowment points are at the same place
• A good allocation is within the edgeworth box, and will depend on the criteria used
• Pareto efficient allocation involves a point that cannot be changed to improve both parties
• Pareto efficient allocation involves maximising utility
• Pareto efficient allocation occurs when the two indifference curves just touch eachother, so are tangent
• Marshallian allocation finds optimal solutions based on the process of goods and consumers budget set
• marshillian allocation maximises utility subject to budget constraints for each consumer
• The budget constraint is the value of endowment
• A competitive equilibrium is a pair of prices and allocations where allocations are optimal given the prices, and markets clear at the prices
• Market clearing bans total demand is equal to total supply
• Competitive equilibrium is Walrasian
• The competitive/ walrasian equilibrium may not be unique
• The first theorem of welfare economics states that the equilibrium point is efficient because both parties maximise with respect to price
• The second theorem of welfare economics is that you can get equilibrium with an efficient outcome
• The edgeworth box allocation can also be justified using game theory and finding the CORE allocation
• for price related optimisation, you set P2 as 1, and P1 as P, as it is the price of good 1 if good 2 costs £1
• when solving price optomisation, you get the allocation and prices of the 2 goods. However, the prices are relative, and involves setting one of the prices as a numeraire (equal to 1)