Which population category equals the sum of employed and unemployed people?

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 a market produces a level of output below the competitive equilibrium, then

A) social welfare is not maximized. B) consumer surplus might still be maximized. C) the actual price will be below the equilibrium price. D) social welfare might still be enhanced if a price ceiling keeps price below the competitive price.