Romeo and Juliet inhabit a pure exchange economy with 1000 units of X and 100 units of Y. Denote Romeo's consumption of X and Y as X_R and Y_R, respectively; denote Juliet's as X_J and Y_J. Romeo's utility function is U^R=X_R Y_R; Juliet's is U^J=X_J ³Y_J. Romeo's marginal utility functions are MU^R_X=Y_R and MU^R_Y=X_R. Juliet's marginal utilities are MUx^J=3X_J ²Y_J and MU_Y^J=X_J ³.

(a) If Romeo (and Juliet) initially owns 500 units of X and 50 units of Y, find the equilibrium price and allocation.

(b) Find the contract curve.