Ralph's responsibility assignment This is a continuation of Demski's problem 19 in chapter 16 (16-19). In attempting to decide whether to evaluate the manager's business unit as a cost center or a cost and revenue center, Ralph and the manager are faced with recognizing or identifying the information structure. Recall cost is either 1 or 2 and revenue is either 4 or 5. Ralph believes if the manager supplies input L then, on average, cost equals 1.7. On the other hand, if the manager supplies input H then, on average, cost equals 1.1, revenue, on average, equals 4.5, and importantly, the product of cost and revenue, on average, equals 4.99.1 The latter quantity acknowledges the idea that encouraging the manager to chase low costs solely may prove detrimental to revenues even if the manager has no direct control over revenues. The manager shares these expected value assessments. Expected value assessments E (c|L] = (P1411 + P15|L) 1+ (P24|L + P25|L) 2 = 1.7 E[CH] = (P14 H + P151H) 1+ (P24|+ P25|H) 2 = 1.1 E [r | H] = (P14|H + P24|H) 4+ (P15| H + P25|H) 5 = 4.5 Elc.r|H] = P14H (1.4) + P15 H (1.5) + P241 H (2.4) + P25) H (2.5) = 4.99 Hence, these common assessments lead to common knowledge (maximum en- tropy) probability assignments. Required: 1. Using maximum entropy probability assignment (see Ralph's probability assignment), identify the joint probability assignment for cost and revenue given the manager supplies input L. That is, determine P14|L, P15|L, P24[L, and P25|L 2. Using maximum entropy probability assignment, identify the joint prob- ability assignment for cost and revenue given the manager supplies input H. That is, determine P14| H, P15H, P24|H, and P25] H. 3. Do you expect Ralph to evaluate the manager's business unit as a cost center or cost and revenue center? Is revenue conditionally informative given the cost measure? Ralph's responsibility assignment This is a continuation of Demski's problem 19 in chapter 16 (16-19). In attempting to decide whether to evaluate the manager's business unit as a cost center or a cost and revenue center, Ralph and the manager are faced with recognizing or identifying the information structure. Recall cost is either 1 or 2 and revenue is either 4 or 5. Ralph believes if the manager supplies input L then, on average, cost equals 1.7. On the other hand, if the manager supplies input H then, on average, cost equals 1.1, revenue, on average, equals 4.5, and importantly, the product of cost and revenue, on average, equals 4.99.1 The latter quantity acknowledges the idea that encouraging the manager to chase low costs solely may prove detrimental to revenues even if the manager has no direct control over revenues. The manager shares these expected value assessments. Expected value assessments E (c|L] = (P1411 + P15|L) 1+ (P24|L + P25|L) 2 = 1.7 E[CH] = (P14 H + P151H) 1+ (P24|+ P25|H) 2 = 1.1 E [r | H] = (P14|H + P24|H) 4+ (P15| H + P25|H) 5 = 4.5 Elc.r|H] = P14H (1.4) + P15 H (1.5) + P241 H (2.4) + P25) H (2.5) = 4.99 Hence, these common assessments lead to common knowledge (maximum en- tropy) probability assignments. Required: 1. Using maximum entropy probability assignment (see Ralph's probability assignment), identify the joint probability assignment for cost and revenue given the manager supplies input L. That is, determine P14|L, P15|L, P24[L, and P25|L 2. Using maximum entropy probability assignment, identify the joint prob- ability assignment for cost and revenue given the manager supplies input H. That is, determine P14| H, P15H, P24|H, and P25] H. 3. Do you expect Ralph to evaluate the manager's business unit as a cost center or cost and revenue center? Is revenue conditionally informative given the cost measure
