Term 1 Week 4: Optimisation and Comparative Statics Flashcards
Where do consumers generally consume (budget constraint and indifference curves) (2)
-Consumers consume where the slope of the budget constraint equals the slope of the indifference curve
-MRS (partially differentiate with respect to x / pd with respect to y) = Px/Py
When does/doesn’t the tangency condition for optimal consumption hold (3)
-If the optimal choice involves an interior solution (both goods), the tangency condition is a necessary condition (not sufficient unless preferences are convex)
-However, a corner solution could mean we don’t have tangency, as MRS < Px/Py for all values
-The consumer will then consume at what corner provides the most utility
What is the Equi-marginal principle (2)
-The principle is that you optimise bundles where the MRS is equal to the price ratio
-The solutions give the Marshallian demands x*(p1, p2, M)
What are the steps for finding your Marshallian demand (4)
-Equal your MRS to your price ratio
-Rearrange this formula to make x1 and x2 … the subject
-Substitute x1 into your budget constraint, then rearrange to make x1 the focus
-This gives you your Marshallian demand for x1
What can you tell about your marshall demand solutions for a cobb-douglas utility function (2)
-These solutions will end up being dependent on income (income effect) and the prices of both goods (substitution effect)
-Your demand for x1 is the exponent multiplied by income, divided by the price (for CD utility functions if the exponents sum to one)
How do consumers optimise for perfect substitutes/complements (2)
-For perfect substitutes, we will likely get a corner solution depending on whether the MRS > Price ratio (x axis) or MRS < Price ratio (y axis)
-For perfect complements, the consumer will optimise at the kink, so we find an expression for an indifference curve at the kink and combine this with the budget constraint
What is the income offer curve (2)
-When income rises, optimal consumption moves, giving the income consumption curve
-If you plot good A on the x axis, all other goods on the Y axis, the income offer curve is the curve which connects your new consumption points as your BC and IC shift outwards
What are the different types of YED goods (3)
-A normal good is one where as price falls, consumption rises, and as income rises, consumption rises
-An inferior good is one where as price falls, consumption rises, and as income rises, consumption falls
-A Giffen good is one where as price falls, consumption falls, and as income rises, consumption falls (a type of inferior good)
What is the Engel curve (2)
-The engel curve has the good on the x axis, and your income on the y axis
-Holding prices constant, this shows how how QD varies with income
What is the price consumption curve (2)
-The price consumption/price offer curve shows us how we shift consumption of a good as price changes
-As our budget constraint pivots outwards for a decrease in price of the x axis good, we explore where our optimal consumption goes
How do we derive the marshallian demand curve, and why is it downwards sloping (2)
-We derive the marshallian demand curve from the price-offer curve, holding everything constant except the price of the good
-The curve is (likely) downwards sloping due to the law of demand, which states that if price falls, demand rises
What are the income and substitution effects (2,2)
-The income effect is that as price falls, the consumers real income rises, they feel more confident so they demand more, so demand rises
-As real income has risen, the consumer moves to a higher IC
-The substitution effect is that as price falls, that good becomes relatively cheaper to consume, so demand rises
-As price falls, the consumer moves on the same IC due to the price ratio change, until they once again reach MRS = price ratio
What are elasticities, and what is our PED formula (1,3)
-Elasticities tell us the responsiveness of one thing to a change in another
-The problem with the traditional PED formula is it tells us arc elasticity, whereas we want point elasticity of demand (PED at a specific point)
-PED = (px/x )(dx/dpx)
-(rate of change of x/x)(rate of change of price/price)
What do XED and YED values mean
-Negative XED = complement, Positive XED = substitute
-The bigger the absolute value of the number, the closer they are in relation
-Positive YED = normal, negative YED = inferior
