Two individuals, Dave and Bob, consume two goods, X and Y. The utility functions for the two individuals are given as: Bob's utility function: UB = 30X^0.25Y^0.75 Dave's utility function: UD = 50X^0.5Y^0.5 Bob is currently consuming 5 units of X and 10 units of Y. Dave is currently consuming 12 units of X and 8 units of Y. The current per-unit prices of X and Y are R10 and R15, respectively.

Question 10:

10.1.1 Determine the marginal rate of substitution for each individual. [4]

10.1.2 In light of the information given above, determine whether the two individuals achieved exchange equilibrium. In your analysis explain (i) if it would be possible to make one individual better off without harming the other and (ii) if the individuals have achieved exchange equilibrium, whether other equilibrium combinations of X and Y between the individuals are possible. [6]