Consider the following values a = 0.50, B = 1, r = 1, u = 0.5, x = 0.70, U - E= 100. As in the Appendix of Lecture 2, the values of being a producer, commodity holder and money holder are given by Vo 6=64.), rta A + BC Vi =( -) (U - ), 1- BD C + AD Vm =( 1-BD)(U e), with B(1 u).x2 A= r+B(1 - 1)x2(72) + Buan* B Burn* r+B(1 u)(472) + Buxn* ? C= B(1-4XII r+B(1 - M.II D=C). r+a (a) Compute Vo, Vi, and Vm for (i) II = 0.80, T* = 0; (ii) II = 0.80, 7* = 1; (iii) II = 0.60, T* = 0; and (iv) II = 0.60, T* = 1. What is the optimal 7* for each II? Explain the results (in less than 3 LINES). (4 Marks) (b) Recently, the UK introduced new 1 pound coins to combat counterfeiting (3 per cent of existing 1 pound coins are fake, according to The Royal Mint). Would your answer to (a) change if there was a positive probability of money being fake? (1 Mark) Consider the following values a = 0.50, B = 1, r = 1, u = 0.5, x = 0.70, U - E= 100. As in the Appendix of Lecture 2, the values of being a producer, commodity holder and money holder are given by Vo 6=64.), rta A + BC Vi =( -) (U - ), 1- BD C + AD Vm =( 1-BD)(U e), with B(1 u).x2 A= r+B(1 - 1)x2(72) + Buan* B Burn* r+B(1 u)(472) + Buxn* ? C= B(1-4XII r+B(1 - M.II D=C). r+a (a) Compute Vo, Vi, and Vm for (i) II = 0.80, T* = 0; (ii) II = 0.80, 7* = 1; (iii) II = 0.60, T* = 0; and (iv) II = 0.60, T* = 1. What is the optimal 7* for each II? Explain the results (in less than 3 LINES). (4 Marks) (b) Recently, the UK introduced new 1 pound coins to combat counterfeiting (3 per cent of existing 1 pound coins are fake, according to The Royal Mint). Would your answer to (a) change if there was a positive probability of money being fake? (1 Mark)