Midterm 1

Question 1

Define economics
Define microeconomics
Define macroeconomics

Answer 1

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

Question 2

Define exogenous variable

Define endogenous variable

Answer 2

Value is taken as given in a model (determined by process outside the model being examined)

value is determined within the model being studied

Question 3

Constrained optimization
Objective function
Constraints

Answer 3

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

Question 4

Define marginal

Answer 4

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

Question 5

Define equilibrium

How is it achieved

Answer 5

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

Question 6

Comparative statics

Answer 6

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)

Question 7

Define positive analysis

What types of questions does it ask

Answer 7

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

Question 8

Define normative analysis

What types of questions does it ask

Answer 8

focuses on issues of social welfare, examining what will enhance or detract from the common good
Asks prescriptive questions (what should be done?)

Question 9

Define utility function

What are the assumptions about preferences

Answer 9

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)

Question 10

Define marginal utility
Formula
How would it be represented on a graph
Relationship between MU and TY

Answer 10

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

Question 11

Principle of diminishing MU

Answer 11

after some point as consumption of a good increases, the MU of that good will begin to fall

Question 12

Power utility family (what is their form and constraints on b)
What is their MU

Answer 12

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

Question 13

When does G(x) have positive, zero or negative MU with what requirements of G’(x)

Answer 13

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

Question 14

Quadratic utility family (what is their form)

What is their MU with constraints on c

Answer 14

every function of the form −(x−c) 2 for some positive c

positive marginal utility at x if and only if x < c

Question 15

Increasing, constant or decreasing MU for G(x) based on G’‘(x)
What would the shape be for G(x)

Answer 15

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)

Question 16

Increasing, constant and decreasing MU for G(x) based on G’(x)

Answer 16

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

Question 17

Increasing, constant or decreasing MU for power and quadratic families based on values of b

Answer 17

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

Question 18

Define increasing, constant and decreasing MU

Answer 18

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

Question 19

What is the budget equation

What is the maximized utility value

Answer 19

Px(x) = I
u = G(I/Px)

Question 20

Define price effect and its direction/sign

Answer 20

Change in consumption that is due to a change in price

Is negative when x = I/Px

Question 21

What is the demand function and it’s derivative wrt Px

Answer 21

x = I/Px

dx/dPx = (d/dPx)I/Px = −I/P^2

Question 22

Define price elasticity and its formula

Answer 22

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

Question 23

Define income effect and its direction/sign

Engel curve function

Answer 23

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

Question 24

Define income elasticity and its direction/sign and formula

Answer 24

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

Question 25

Define income effect on utility and its sign/direction | Income to utility function

Answer 25

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

Question 26

Define price effect on utility and its formula and its direction/sign

Answer 26

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.

Question 27

Define compensation variable and its formula Define compensation variable if the opposite change is happening What is Ic

Answer 27

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

Question 28

Define equivalent variation and its formula | Define equivalent variation if the opposite change is happening

Answer 28

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)|

Question 29

Define the approximate change in consumer surplus | Define it if the opposite change is happening

Answer 29

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

Question 30

Define budget constraint | Define budget line

Answer 30

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

Question 31

How do changes in income and price affect the budget line

Answer 31

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

Question 32

Define consumption basket | Define price ratio and what it means

Answer 32

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

Question 33

What is a basket graph and iso expenditure line

Answer 33

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 ```

Question 34

Formula for total utility of basket (x,y)

Answer 34

G(x) + H(y)

Question 35

Marginal rate of substitution depending on G'(x) or H'(y) | What it means (5)

Answer 35

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

Question 36

Conditions for quadratic quasilinear TU What is MRSxy for quadratic quasilinear TU

Answer 36

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 ```

Question 37

Conditions for twin power TU with unit coefficients MRSxy for twin power TU

Answer 37

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)

Question 38

Direction of change in MRSxy

Answer 38

When b<1: MRSxy is decreasing in x/y When b>1: MRSxy is increasing in x/y

Question 39

Speed of change in MRSxy (how to find it and the formula) Ratio elasticity of MRSxy

Answer 39

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

Question 40

Complement goods Substitute goods When does a perfect substitute occur When does a perfect complement occur

Answer 40

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

Question 41

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

Answer 41

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)

Question 42

Perfect substitutes for twin power TU functions with general coefficients

Answer 42

Tf and only if there as positive coefficients a1 a2 such that g(x) + h(y) = a1x + a2y