Econ 4001.02 Test #2

D, fk(x,x) - K could be positive (increasing) negative (decreasing) or 1 (constant)

D) For returns to scale Cobbs Douglas: a+b. For marginal product, take partial derivative of x, look at sign where (+) means increasing

B) For this question, only need to solve for first value, plug in the multiplier and simplify

A)

B - thats what moving along an isoquant does

C - MPx or MPy are dependent on q

D - Slope of isoquant changes

C)

Factors out to k^bc. Compare that value to 1

D)

(p)(MP) = w (equilibrium, if higher the firm would hire more and vice versa)

1. Find MP of q

2. Use equation above

3. Substitute

C

Dumb Question

MP x P = w

Find MP, multiply by price of output and substitute

C)

1. Find MRTS (Use cobbs douglas trick)

2. Set equal to price ratio

3. Cross multiply

D)

1. Identify that these are perfect substitutes

2. Find MP of each

3. plug into MP x P = w, solve for x

4. Larger number = more output, plug that # into original function

• DONT plug into both

• 
  

B)

Set MRTS = to w1/w2

“3 Times” = 3x/x etc.

Cross multiply

C)

Find MC of each

set them equal to eachother and solve for y1

y1 + y2 = # of units

plug in y2 for y1, solve

B)

Recognize Cobbs-Douglass formula

Z^ ½ and (x + y)^ ½ both receive same amount

B)

Recognize the minimum - choose lower number

Add corresponding numbers

B)

Find MRTS

Set MRTS = Price ratio

Cross multiply, find relationship between M and L

Use initial function, put M in terms of L and set equal to total value produced

• Find the value of L

Find M with new value of L

Plug into TC Functions (wL x L) + (wM x M)

A

Plug 4 in for M (states machines cannot change) to solve for L

Plug into TC function (wL x L) + (wM x M)

C)

Take integral ( + C is fixed cost)

plug in

D)

A - MC rises before even intersecting

B - MC rises afterwards as well

C - MC > ATC after minimum points (where it begins to rise)

A)

MC = P

B)

+ x is fixed cost

Divide q from VC to find AVC

Plug in 10

C)

Set P = ATC

Divide out TC by q to find ATC

Plug in values and solve for Q

C)

Set MRTS = Price Ratio

x1 in terms of x2

Plug back into production function (can split up #x2 to (#^) (x^)

• Solve for y, put in terms of x2

  • Plug that value back into x1 = 36x2 (x2 part replaced) to find relationship between y and x1

• Using the two relationships (x2 and y, x1 and y) plug back into production function and add

Take derivative of TC

B)

Short-run constraint, plug in value fo X2

Solve for X1

• Plug into SRTC Function and simplify to find TC

Take derivative for MC

Question was flawed: makes more sense if it is 7q² + 175q

Find MC

• Use to find supply curve (y=p/4)

Find AC, then take derivative and set = 0

• Use that y value to plug back into AC

Short-run, operates if P > AVC

D)

Calculate the cost per cup for wages

• add number to Pc

C)

Find MC of firm 1, plug in q

• Set this value = MC of firm 2 and solve

A)

Realize its Compliments, x1 = 5x2

Set each = y (output values) and solve for x =

C = w1x1 + w2x2

• Plug in values to solve in terms of y for cost

Find MC

Remember P = MC

Solve for y in terms of p

Find AVC of each (divide q from VC)

Find Derivative, set = 0

Plug Q back into AVC function to find AVC

Compare that AVC to value given for Market Price of sunglasses

C)

Find TC (given $ x [p x kilometer])

• Find profit, (given $ - found value)

Multiply profit by total number of jars

B)

Find AC (divide q)

Find MC (take derivative)

Set AC = MC, find quantity for each firm

Find P = MC (already solved MC), plug in above value for Q

Plug value of P into Q function

Divide Qd/# of firms (found above)

A

D)

Invert Supply Curve

Take integral of p =

B)

Find MC of each term

Set equal to p, form: y = xP

Multiply by # of firms by value

Add the two together

B)

Set supply = demand

B)

Set supply = demand

Set supply (+ tax) = demand

Find difference

Set supply = demand

Set supply = demand (+ tax)

Find difference

Plug in values to DWL formula (½)(t)(Change in Q)

A)

Price floor = Insufficient Demand and too much supply

Plug in p, subtract

B)

DWL = ½ (2t) (Qt)

• Here, doing anything to t also impacts Q, therefore impact is larger

a)

Just plug in

b)

Set function = 8

Simplify, put in terms of K

c)

Cobbs Douglas Trick

• means that firm can substitute 2 units of labor for 3 units of output and remain at the same level

d)

L = decreasing, derivative has a negative exponent

K = decreasing negative exponent

e)

Cobbs-Douglass, when exponents = 1, constant returns to scale

a)

Short run profit function; py - wL - rK

• Plug in values, y = min{} (plug in K value as well)

b)

• Plug in prices and values into previous equation

• Answer: 12

c)

Compare prices of L, anything below 7 leads to a loss per worker added, the firm would not hire any

PERFECT SUBSTITUTES

a)

Plug in values for L and K

b)

Produce 100 with the cheaper option, (divide 100 by coeffecient)

c)

Compare new costs per unit

• They are equal, any amount works

pt.1

a)

Find TRS and set equal to Price Ratio (w/r)

b)

Plug in L=… to initial function and isolate for K

Plug in K=… to initial function and isolate for L

c) fade

pt. 2

d)

Find quantity of labor and capital using the firms long run conditional demand functions for L and K

Multiply those values by the prices to get C

Add together

e)

Keep K constant this time and solve for L (using conditional demand function for L)

Multiply those values by the prices to get C

Add together

Set equal to output level

Use exponent so that one variable is itself

Divide out

B

C

A + B both act as if its a preference curve. Instead, with production functions, multiplication actually changes the technology involved (bc more had to be produced from somewhere)

B

• P = MC, so the firm will increase MC to get to new P, meaning output is increasing

A - “every” isnt necessarily true

C - Higher P = Higher profits

D - This is not true, the MRTS varies

Prices “between” 7 and 10 (aka not 7 or 10)

• This means S3 will produce and S2 will not. S1 also produces

Add S3 and S1