Test #1, Econ 4001.02

Steps:

1 - Isolate k

2 - Must be a or c because of the nature of an indifference curve

3 - Plug in sets, see which k is higher

ANSWER: a

Steps

1 - Define Terms

• Monotonic: more is always better than less

• Convex: idea that you would settle for less quantity of x if it were mixed with y rather than stand alone. (Why indifference curves are bent)

ANSWER: C

1 - Find derivative to find slope

2 - Plug in X1; (X2 is like finding dy in calc)

ANSWER: A

1 - Define Terms

• Completeness: A consumer can rank bundles based on preference

• Reflexity: Any bundle is as good as itself

• Transivity: A > B and B > C, So A > C

• Substituitivity: Not a standard word; the degree to which one good can replace another and maintain utility

ANSWER: C

1- Find MRS (MUx/MUy)

2 - Set MRS = Price Ratio. (Because it is where the slopes are equal - for well behaved only)

3 - Solve for y = ax

4 - Plug ax into budget constraint for y

5 - Plug in numbers

ANSWER: D

1 - Find MRS (MUx/MUy)

2 - Plug in given values

3 - Do some algebra and solve. Assume the MRS is negative here

ANSWER: C

1 - Take out a divisible number so that the values are equal

2 - Identify that the equations are now the same with the only difference being the factor of U

3 - Identify that this is a perfect complement, so factor of U does not matter, instead only the kink points do

ANSWER: A

1 - Identify that the question is about MRS at the optimal point

2 - MRS at optimal point = price ratio

3 - SAME PRICES, Even if income is different, slope will be the same

Layup

1 - Solve for initial utility through substitution

2 - New price for x, set equal to new U

3 - Solve for y

Plug in each person’s values to the other equations and compare

1 - Solve for the square

2 - ²indicates monotonic

3 - The (x + 4y) is perfect substitute

4 - perfect substitute is straight like

ANSWER: B

1 - Must simplify to (x^a)(Y^a)

2 - work inversely with log functions to solve

ANSWER: D

1 - Plug in initial numbers and find U

2 - Divide U by x and find y

ANSWER: D

1 - Identify “Fixed Propoirtions”; these means perfect substitutes.

2 - Bc of this, Ax = Bx

ANSWER: C

1 - Homothetic; MRS stays constant / consumption of all goods stays proportional

2 - Multiply goods bought by correct factor

ANSWER: A

1 - Identify “Income Offer Curve”, when m increases what happens to consumption of X2 and X1

2 - Evaluate each function:

• X2, value is just the price ratio, which does not change

• X1, as long as m > 2 (which it specifies), it will increase

3 - graph it out

ANSWER: B

1 - A cannot be correct because perfect substitutes are “all-or-nothing” whatever is the highest U/$ would have 100% allocation

2 - B cannot be correct, he will buy more if his income increases

3 - C cannot be correct, that is indicative of a perfect compliments

4 - Cobbs-Douglass has everything purchased in fixed percentages. Depicted by the exponents

ANSWER: D

1 - Identify function is Quasilinear

2 - Recall Engel Graph properties; once X1 is saturated, the remaining will be directed towards X2

ANSWER: 10

1 - Identify that this is a perfect compliment function

2 - Calculate U currently by plugging in numbers

3 - Find lower of the 2 values

4 - Solve for what x and y could be to = 20

5 - Multiply those values by the price

ANSWER: C

1 - Find where q = 0 (price on y axis)

2 - Graph p1 and p2

3 - Find q with current price

4 - graph out, use ½ (b)(h) to find CS

1 - Find where q = 0 (for top price) and plug in p to see what q1 is equal to

2 - Do the same for q2

3 - Use triangle graph and solve

1 - Find derivative of the function

2 - Rearrange so it is x = ___ (A demand function)

3 - continue with surplus graphing

ANSWER: A

A

1 - PxX1 + PxX2 = M

ANSWER: (10)(q1) + (6)(q2) = 120

• Graph out as well, with x2 on y and x1 on x

B

1 - Adjust original budget constraint

ANSWER: (14)(q1) + 6(1.0175q2)

• Graph out as well

A

1 - IDENTIFY THAT THIS IS PERFECT SUBSTITUTES

2 - Write a standard utility function:

ANSWER: U(H,D) = H + 3D

3 - Graph out perfect substitutes:

ANSWER: Straight line, (x2 = 9, x1= 3) (x2 = 6, x1 = 2) (x2 = 3, x1 = 1)

B

1 - perfect substitute demand function: MU/P

ANSWER: 3/Ph, 1/Pd

C

1 - Because it is perfect compliment, find item with highest U/$

2 - Buy only that item

ANSWER: 20 hot dogs, 0 hamburgers

A

1 - IDENTIFY THAT THESE ARE PERFECT COMPLIMENTS

2 - Draw the 90-degree indifference curves

B

1 - Draw the budget line; divide 18 by 2 and 3, respectively

2 - Solve for the optimal point by putting x in terms of y (can do this because the two goods are bought in pairs

3 - Plug that value into the budget constraint formula. Solve for y

4 - use y to solve for x

ANSWER: (6,2)

C

1 - Demand functions for perfect compliments: m / (p1 + p1)

2 - must need 3 times are much x to get same utility as y; so bottom is 3px + py

3 - For y keep m alone

4 - For x, multiply bundle by 3 to find the true quantity of x

ANSWER: y = m / 3px + 3py, x = 3m / 3px + 3py

D

1 - 60 units of x means 20 units of y

2 - plug into budget constraint to find total m

ANWER: 320

A

1 - find the partial derivatives of R and M

ANSWER: R = 4M^-1/2, M = 4

2 - Divide MUR/MUM

ANSWER: Simplifies to -1/R^1/2

B

1 - Set MRS = Price Ratio

2 - Solve for R

3 - Plug R back into budger constraint and solve for M

ANSWR: M = 8

C

1 - Plug in 36 for R

2 - Price ratio = 1/6

A

1 - Solve Partial derivatives for both (remember multiplication rule)

2 - Use the Cobb-Douglas simplifier (-ay/bx) to find MRS

3 - Simplify MRS

ANSWER: C/2B

B

1 - Set MRS = Price Ratio

2 - Put the value into terms of B

3 - Plug into Budget Constraint

4 - solve for B, then once you have that value, solve for C

ANSWER: B = 4, C = 6

A

1 - Budget Constraint: pxX + pyY = m

2 - Find demand function for C and B: put one into terms of the other

• Start by finding the MRS (use the Cobb-Douglas trick)

  • Set equal to price ratio of Pc/Pb

• Plug PbB (now in terms of C) back into budget constraint to find C’s function

• Do the inverse but with PcC in terms of B

  • Add both terms in ratio together; divide by 5Pb/3

ANSWER: B = 3m/5Pb

C = 2m/5Pc

B

1 - Chug and Plug

2 - Values here should be (3,3) (6,6) (9,9)

ANSWER: graph values with simple x=y

C

1 - plug in pc to demand function and simplify

2 - move m to other side, m = 5C

3 - That is your engel curve function

ANSWER: Normal good

All parts

Simple

A

B

C

D