Which of the following is a type of ownership that features a fixed payment?

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.

If nominal GDP increased from $4,500 billion in 2010 to $5,000 billion in 2011 and the GDP deflator increased from 100 to 105 over the same time period, what would the 2011 real GDP equal expressed in terms of 2010 dollars?

a. $4,285 billion b. $4,500 billion c. $4,725 billion d. $4,762 billion