Midterm 1 Flashcards
Define economics
Define microeconomics
Define macroeconomics
Science that deals with the allocation of limited resources to satisfy unlimited wants
Economic behaviour of individual economic decision makers
Analyzes how a national economy performs
Define exogenous variable
Define endogenous variable
Value is taken as given in a model (determined by process outside the model being examined)
value is determined within the model being studied
Constrained optimization
Objective function
Constraints
Is used when making the best/optimal choice, taking into account any possible limitations/restrictions on the choice
Relationship that a decision maker seeks to maximize or minimize
Restrictions/limits imposed on the decision maker
Written as: maxObjectiveFunction
(endogenous variables)
subject to: xxx
Define marginal
How a DV changes as a result of adding one more unit of IV
Measures the incremental impact of the last unit of the IV on the DV
Aka rate of change
Define equilibrium
How is it achieved
state/condition that will continue indefinitely as long as exogenous factors remain unchanged
In a competitive market, equilibrium is achieved at a price where the quantity supplied equals the quantity demanded
Comparative statics
Used to examine how a change in an exogenous variable will affect the level of an endogenous variable in an economic model
Allows us to do before and after analysis of a model (initial exo values v.s. Changed exo values, impact on endo values)
Define positive analysis
What types of questions does it ask
Attempts to explain how an economic system works or to predict how it will change over time Asks explanatory (what has happened?) or predictive (what will happen?) questions
Define normative analysis
What types of questions does it ask
focuses on issues of social welfare, examining what will enhance or detract from the common good
Asks prescriptive questions (what should be done?)
Define utility function
What are the assumptions about preferences
measures the level of satisfaction a consumer receives from any basket of G/S
Can represent preferences (assumed to be complete, transitive, and that more is better)
Define marginal utility
Formula
How would it be represented on a graph
Relationship between MU and TY
the rate at which total utility changes as the level of consumption rises
MU of y = change in U/change in y
Graphically, MU at one point is represented by slope of that point’s tangent
MU is slope of TU
Principle of diminishing MU
after some point as consumption of a good increases, the MU of that good will begin to fall
Power utility family (what is their form and constraints on b)
What is their MU
collection of functions having the form G(x) = −x^b for negative b, the form G(x) = ln(x), or the form G(x) = x^b for positive b
Every member has positive MU everywhere
Positive MU = utility increases with consumption
When does G(x) have positive, zero or negative MU with what requirements of G’(x)
G has positive marginal utility at x if and only if G’(x) > 0
G has zero marginal utility at x if and only if G’(x) = 0
G has negative marginal utility at x if and only if G’(x) < 0
Quadratic utility family (what is their form)
What is their MU with constraints on c
every function of the form −(x−c) 2 for some positive c
positive marginal utility at x if and only if x < c
Increasing, constant or decreasing MU for G(x) based on G’‘(x)
What would the shape be for G(x)
G(x) has increasing marginal utility if and only if G’’(x) > 0 for all x, which happens if and only if G(x) is strictly convex (curve opens upwards)
G(x) has constant marginal utility if and only if G’’(x) = 0 for all x, which happens if and only if G(x) is both weakly convex and weakly concave
G(x) has decreasing marginal utility if and only if G’’(x) < 0 for all x, which happens if and only if G(x) is strictly concave (curve opens downwards)
Increasing, constant and decreasing MU for G(x) based on G’(x)
G(x) has increasing marginal utility if and only if G’(x) is increasing
G(x) has constant marginal utility if and only if G’(x) is constant
G(x) has decreasing marginal utility if and only if G’(x) is decreasing
Increasing, constant or decreasing MU for power and quadratic families based on values of b
Each member of the power-utility family, with b<0, has decreasing marginal utility
Each logarithmic member of the power-utility family has decreasing marginal utility
Each member of the power-utility family, 0 < b < 1 has decreasing MU
Each member of the power utility family with b=1 has constant MU
Each member of the power utility family with b > 1 has increasing MU
Each member of the quadratic utility family has decreasing MU
Define increasing, constant and decreasing MU
Increasing marginal utility means that the incremental utility from another unit of consumption is increasing with consumption
Constant marginal utility means that the incremental utility from another unit of consumption does not change with consumption
Decreasing marginal utility means that the incremental utility from another unit of consumption is decreasing with consumption
What is the budget equation
What is the maximized utility value
Px(x) = I u = G(I/Px)
Define price effect and its direction/sign
Change in consumption that is due to a change in price
Is negative when x = I/Px
What is the demand function and it’s derivative wrt Px
x = I/Px
dx/dPx = (d/dPx)I/Px = −I/P^2
Define price elasticity and its formula
Derivative of the demand function, in percentage terms
ε = (dx/dPx)(Px/x) = (−I/Px^2 )(Px/(I/Px)) = −1
^^uses demand function and it’s derivative
1% increase in price Px results in a 1% decrease in consumption x so that expenditure Pxx remains constant at I
Define income effect and its direction/sign
Engel curve function
A change in consumption that is due to a change in income
Is positive when x = I/Px
dx/dI = (d/dI)I/Px = 1/P
Define income elasticity and its direction/sign and formula
derivative of the Engle-curve function, in percentage terms –> income effect in percentage terms
η = (dx/dI)(I/x) = (1/Px)(I/(I/Px)) = 1
1% increase in income I results in a 1% increase in consumption x so that expenditure Px(x) increases with, and remains equal to, I
Define income effect on utility and its sign/direction
Income to utility function
A change in utility that is due to a change in income
du/dI = dG(I/Px)/dI = G’(I/Px) · d(I/Px)/dI = G’(I/Px) · (1/Px)
income effect on utility is positive exactly when marginal utility is positive
Define price effect on utility and its formula and its direction/sign
A change in utility that is due to a change in price
d/dPx G(I/Px) = G’(I/Px) · d/dPx (I/Px) = G’(I/Px) · (−1/Px^2)
the price effect on utility is negative exactly when marginal utility is positive.
Define compensation variable and its formula
Define compensation variable if the opposite change is happening
What is Ic
The additional income which would compensate the consumer for the increased price
|CV| would be the income loss that would make the consumer just as poorly off at the new lower price as they were at the old higher price
|CV| = |Ic − Ia| = |Pbx (Ia/Pax) − Ia|
Ic is the total income that would generate old utility G(Ia/Pax) at the new B price
Define equivalent variation and its formula
Define equivalent variation if the opposite change is happening
The loss in income which would, at the old price, result in the new utility
|EV| would be the income gain that would make the consumer just as well off at the old higher price as they are at the new lower price
|EV| = |Ie − Ia| = |Pax(Ia/Pbx − Ia)|
Define the approximate change in consumer surplus
Define it if the opposite change is happening
The area below the demand function between Pa and Pb
Is the extra expenditure on the units still bought, plus the value lost on the units no longer bought
The expenditure saved on the units previously bought, plus the value gained on the new units bought
|∆CS| = [|Pbx −Pax|(xb+xa)]/2
Define budget constraint
Define budget line
The set of baskets a consumer can purchase with limited income
Px(x) + Py(y) less than or equal to I
Set of baskets a consumer can purchase when spending all of their available income
Px(x) + Py(y) = I
How do changes in income and price affect the budget line
Increase income = shifts line outward parallel
Decrease income = shifts line inward parallel
Increase price = moves intercept of that good’s axis closer to origin
Decrease price = moves intercept of that good’s axis further from origin
Define consumption basket
Define price ratio and what it means
Pair (x,y) of non negative values
Px(x) + Py(y)
Price ratio = Px/Py
It means:
Price of x relative to price of y
Price/market value of x in terms of price of y
How much you need of y to buy one unit of x
How much you get of y from selling one unit of x
What is a basket graph and iso expenditure line
Instead of representing each basket (x,y) as points, each basket is a small circle containing the basket’s expenditure
Iso expenditure line = line consisting of baskets having the same expenditure Have the form e = Px(x) + Py(y) slope = negative of price ratio A specific (x,y) basket can only be on one line, all baskets on one line have the same expenditure
Formula for total utility of basket (x,y)
G(x) + H(y)
Marginal rate of substitution depending on G’(x) or H’(y)
What it means (5)
G’(x)/H’(y) if H’(y) =/= 0
888 if G’(x) > 0 and H’(y) = 0
Undefined otherwise
MUx/MUy
MU of x relative to MU of y
MU of x in terms of y
Personal value of x in terms of y
How much y feels the same as getting one unit of x
How much y feels the same as losing one unit of x
Conditions for quadratic quasilinear TU
What is MRSxy for quadratic quasilinear TU
If and only if: G(x) = -a(x-c)^2 for a positive a and a positive c
H(y) = y
MRSxy = G’(x) / 1 = -2a(x-c) MRSxy = 0 when x = c
Conditions for twin power TU with unit coefficients
MRSxy for twin power TU
If and only if: There is a negative b such that G(x) = -x^b and H(y) = -y^b
Or: G(x) = ln(x) and H(y) = ln(y)
Or: there is a positive b such that G(x) = x^b and H(y) = y^b
MRSxy = (x/y)^(b-1)
Direction of change in MRSxy
When b<1: MRSxy is decreasing in x/y
When b>1: MRSxy is increasing in x/y
Speed of change in MRSxy (how to find it and the formula)
Ratio elasticity of MRSxy
Derivative of MRSxy function would tell us rate at which MRSxy is increasing/decreasing/staying constant with respect to x/y
Formula: d(MRSxy)/d(x/y)
Ratio elasticity of MRSxy is the derivative times (x/y)/(MRSxy)
Will equal b-1
Complement goods
Substitute goods
When does a perfect substitute occur
When does a perfect complement occur
Complements: if MRSxy declines quickly as x/y increases
Substitutes: if MRSxy changes slowly as x/y changes
Perfect substitute occurs when b=1 because ratio elasticity = 0 so MRSxy does not change with x/y
Perfect complement is as b approaches negative infinity
Conditions for twin power TU with general coefficients
MRSxy for twin power TU with general coefficients
What happens when you change the coefficients
Effect of coefficients on ratio elasticity
If and only if: there are negative b and positive ax such that G(x) = -ax^b and H(y) = -ay^b
Or: there are positive a1 and a2 such that G(x) = a1ln(x) and H(y) = a2ln(y)
Or: there are positive b, a1, and a2 such that G(x) = a1x^b and H(y) = a2x^b
MRSxy = (a1/a2)(x/y)^(b-1)
Doubling coefficient a1 doubles MRSxy
Doubling coefficient a2 halves MRSxy
Coefficients have no effect on ratio elasticity of MRSxy (still = b-1)
Perfect substitutes for twin power TU functions with general coefficients
Tf and only if there as positive coefficients a1 a2 such that g(x) + h(y) = a1x + a2y
