• We know all the sets of quantities that consumers are willing to purchase under given prices.
• We know all the sets of quantities that producers are willing to produce under given prices.
• How much will be sold and at which price?

• If the market price is on the level, such that demand is higher than supply, shortage of the goods occur.
• It leads other firms to enter the market, or the existing firms to produce more.
• Speculators enter the market to sell the goods over the counter.
• In both cases, prices go up.

• If market price is on the level, such that demand is lower than supply, surplus of the goods occur.
• It leads other firms to exit the market, or the existing firms to cut the production.
• As a result, prices go down.

• Market equilibrium occurs when the quantity demanded equals the quantity supplied, or when buyers' and sellers' plans are in balance.
• We define equilibrium in terms of equilibrium price and equilibrium quantity.
• When market is in equilibrium, there are no surplus or shortage, market demand matches market supply.

• When demand changes, the demand curve shifts and market turn into disequilibrium.
• Under the old price, either a surplus or a shortage will occur, driving a price either up or down.
• To match new demand, suppliers (or speculator) readjust the price and quantity accordingly.
• The new price quantity will be a new equilibrium.

• Similarly, when supply changes, the supply curve shifts which causes market to enter disequilibrium.
• Now the market either has a shortage or a surplus, which causes price to change.
• To match new supply, demand will readjust price and quantity
• The new price-quantity will be a new equilibrium.

• Suppose demand and supply for good X is given by the following demand and supply functions:

\[ P=2Q_s+1\\ P=9-2Q_d \]

• Find an equilibrium.
• A substitute for a good X became more affordable, which caused shift to the demand function to \(P=5-2Q_d\). Find new equilibrium.
• Rising interest rates for corporate loans cased supply curve to shift to \(P=2Q_s+5\). Find a new equilibrium for: a) before demand shift. b) after demand shift.

• Demand is defined by the following function
• \(P=6-3Q_d\)
• Supply is defined by the following function
• \(P=3Q_s\)
• 1. Draw the demand and supply curves and find an equilibrium.
• 1. Suppose after demand and supply shift, the new demand curve is \(P=10-3Q_d\) and the new supply curve is \(P=3Q_s-2\). Draw the shift on the same graph and find new equilibrium.

• Given the supply and demand functions we can find and analyze the equilibrium price and quantity in the given market.
• Each side of the market however is defined by the individual agents who make decisions acting in their self-interest.
• Market has a cyclicity. Agents' choices that depend on aggregate factors (price, state of the economy) and individual factors (preferences, personal income) form an individual market demand, that in turn define the state for the aggregate factors.

• Demand side is defined by the individual agents that are acting as consumers endowed with a certain individual wealth (from factors of production) and trying to maximize their benefit by consuming goods satisfying their preferences.
• Agents have dual nature with the link of wealth - they consume goods by spending it and earn it by using factors of production.
• Agents are rational in a sense of maximization of their benefits, i.e. we can have different agents with different preferences, but if we know the structure of it, we can calculate their demand.

• Given the sets of goods available to the consumer, preferences define an order in which consumer rank them in terms of their benefit.
• Practically, when we observe a consumer purchasing a set of goods when the other sets are available to her, we say that she revealed her preferences. Preferences change over time.
• Preference theory usually based around axioms of transitivity and completeness.
• Axiom of transitivity implies that the order of preference is consistent. If you prefer set A to set B, and set B to set C, you must prefer set A to set C.
• Axiom of completeness states that we can order any set, meaning that if you have two sets A and B, one of three must be true: you prefer A to B, B to A, or you are indifferent between them.

• To quantify the preference, we use utility function - a function \(u(x)\), where \(x\) - quantity of a good (or a set of goods).
• Utility function is upward sloping (increasing), which shows the increasing benefit of consuming more of the good.
• Utility is also concave, which indicates that each additional unit of the good bring less benefit than the previous one. We assume there is a point of saturation.
• In case of uncertainty, a concave utility function shows a risk-averse behavior, i.e. preferring a certain outcome to a similar uncertain.

• Utility function itself does not measure preferences directly, but rather serves as an abstraction layer to quantify preferences.
• Cardinal utility measures a magnitude of the benefit received by consuming a certain set.
• Ordinal utility measures an order of the goods irrespective of the location and scale.
• Unlike cardinal utility, a value of ordinal utility has no intrinsic meaning. For example, if a consumer can purchase three goods A, B, and C, and utility functions \(u(A)=9,\, u(B)=8,\,u(C)=1\) and \(u(A)=9,\, u(B)=2,\,u(C)=1\) would describe the same preference, because the order is preserved.

• Like PPF, if we have two goods, we can draw a curve that corresponds to all combinations that award the same utility. This curve is called indifference curve.
• Mathematically, indifference curve is a function \(u(x,y)=C\), where \(x\) and \(y\) are quantities of the good, and \(C\) is a value of utility function.

• Each consumer can only spend the amount of wealth she currently possess.
• If there are two goods \(A\) and \(B\) available with the prices \(P_A\) and \(P_B\), and consumer's total income is \(I\), then we can write budget constraint as \(P_A A+P_B B=I\).
• In the space of quantities \(A\) and \(B\), it is a linear function.

• When making decisions, a consumer want to choose an indifference curve with the highest utility, that will satisfy her budget constraint. The indifference curve will be tangent to the budget constraint.
• We can change the price of one of the goods to see how optimal decision changes. The budget constraint will shift, so will the optimal decision.
• If we account for all possible prices, we can draw the individual demand curve for this consumer.

• Consumer utility function for goods \(x\) and \(y\) is defined as follows: \(u(x,y)=y+2x\). The budget constraint for the consumer is given by: \(x+y=10\), i.e. \(P_x=P_y=1\). Find individual quantity demanded for this consumer.
• Suppose the price of \(x\) went up to \(P_x=1.5\). Find the new quantity demanded.
• The price of \(x\) is now \(P_x=3\). What is the quantity demanded? Approximate the individual demand curve.

• We considered a competitive market and defined a point of equilibrium.
• We draw parallels between the production economy (PPF) and the distribution economy (a competitive market).
• We showed how individual consumer decisions lead to the individual demand.