Nonlinear price discrimination A) sets the price consumers pay ...

[kellyjaisingh]

Nonlinear price discrimination
 
  A) sets the price consumers pay based on quantity purchased.
  B) is where the firm sets prices in geometrically or exponentially decreasing price points.
  C) is used in situations where consumers have no reservation prices.
  D) eliminates deadweight loss.

Question 2

Rachel spends her income, Y, on Rock Shows (R) and Sunglasses (S) with prices pR and pS. Rachel's preferences are given by the Cobb-Douglas utility function
 
  U(X,Y) = R.8S.2
  a. Write out the Lagrangian for Rachel's utility-maximization problem.
  b. Use the Lagrangian to derive Rachel's optimal choice, (R,S).
  c. For a given utility level, U0, derive Rachel's Expenditure function E(pR,pS,U0).
  d. Use the Expenditure function to derive Rachel's compensated demand for Rock Shows.

Question 3

Food stamps are ______.
 
  a. financed by the federal government but administered by the states
  b. financed by the federal government and the states and administered by the states
  c. financed by the federal government and the states and administered by localities
   d. financed by the states but administered by the counties

[Melissahxx]

Answer to Question 1

A

Answer to Question 2

a. The Lagrangian is
L = R.8S.2 + Y  pRR  pSS
b. The necessary conditions for utility maximization
LR = .8R-.2S.2  pR = 0
LS = .2R.8S-.8  pS = 0
L = Y  pRR  pSS = 0
The first two conditions above yield the MRS = MRT condition:
4S/R = pR/pS
Solve to get S = R(pR/4pS)
Plug into the 3rd condition above (the budget constraint) to get
Y = pRR + pRR/4 = 5pRR/4
Solve for the demand equations:
R = 4Y/5pR
S = Y/5pS
c. Using the Lagrangian for the corresponding minimization problem:
L = pRR + pSS + U0  R.8S.2
The necessary conditions are
LR = pR  .8 R-.2S.2 = 0
LS = pS  .2R.8S-.8 = 0
L = U0  R.8S.2 = 0
The first two conditions yield:
4SpS = RpR
which is the same as in part b. Substituting into the expenditure expression we get
E = pRR + pSS = pRR + pRR/4 = 5pRR/4
Rearranging terms we get
R = .8E/pR
And similarly
S = .2E/pS
The indifference curve expression yields
U0 = (.8E/pR).8(.2E/pS).2
Rearranging, we get
E = U0(pR/..8(pS/.2).2

d. Taking the derivative of the expenditure function with respect to pR:
R = E/pR = (.8pS/.2pR).2U0

Answer to Question 3

a