What is the equation for optimisation
A tangency between IC and budget constraint
MUx/MUy = Px/Py
Corner Solutions
If the MRS < Px/Py for all P, with diminishing MRS, the slopes will never be equal so the consumer will optimise while consuming one good only, tangency condition doesn’t hold
Non-convexity
Tangency condition is necessary for optimality but not sufficient unless preferences are convex. Tangency is not always optimal, optimal points are on the highest IC which is tangential to the budget constraint
Equi-marginal principle
Optimising the bundle by setting MRS equal to price ratio and using the budget constraint to find Marshallian demands
Marshallian demands of perf subs
x1 = M/P1 if MRS> p1/p2
x1 = 0 ≤ x1 ≤ M/P1 if MRS = p1/p2
x1 = 0 if MRS < p1/p2
Marshallian demands of perf complements
x* = M/(P1 + P2), consumer will optimise at kink
Income-offer curve
Graphically shows changes in income and the movement of optimal consumption
Engel curve
Derived from the income-offer curve, shows how quantity demanded varies with income while fixing prices. Can slope up or down for different types of goods
Demand Curves
Derived from the price-offer curve, fixing income, preferences, and other prices it shows how quantity demanded changes following a price change
Income and substitution effect
Sub: As the price of good X goes down, good Y becomes relatively more expensive and less attractive
Income: As the price of good X goes down, real income rises so the consumer feels richer and demand changes
Price elasticity of demand (PED)
Measures how much demand changes from a change in price.
Ex = dx/dPx multiplied by Px/x
Income elasticity of demand
The change in demand in response to a change in income.
= dx/dM multiplied by M/x
Cross price elasticity of demand
Change in demand in response to changes in the price of another good
= dx/dPy multiplied by Py/x
