a) 13) QUESTION 4 [80 Points] [10 Points] Suppose that a consumer has the utility function U = f(q1) + q; where good 2 = \"all other goods\". Making suitable assumptions, prove that the consumer will buy good 1 so long as the C S from good 1 is > 0. \"Derive\" your answers by showing all steps / calculations and stating all assumptions. [10 Points] Suppose a market consists of 10 \"Type1\" customers each of whom has the utility function (good 2 = all other goods): ((11 '11): U = + 2 B QZ And 5 \"Type2\" customers each of whom has the utility function: 2 a _ U = _ ( 2 '71) + Q2 Z' Assume 6:2 > all > constant > 0. Derive an individual Type1 customer's demand function of good 1 and an individual Type2 customer's demand function of good 1. \"Derive\" your answers by showing all steps / calculations and stating all assumptions. [10 Points] Suppose that a monopolist sells \"good 1\" to Type 1 and Type 2 customers by charging twopart tariffs. Assume the MC of serving a Type1 customer is equal to the MC of serving a Type2 customer. Recall that there are 10 \"Type1\" customers and 5 \"Type2\" customers. Assume the company & identify whether a particular customer is a Type1 or a Type-2 customer. Derive the optimal two-part tariff scheme (assume a common usage price that is initially > MC). \"Derive\" your answers by showing all steps / calculations and stating all assumptions. d) [20 Points] Suppose that a monopolist sells \"good 1\" to Type 1 and Type 2 customers by charging twopart tariffs. Assume the MC of serving a Type1 customer is equal to the MC of serving a Type2 customer. Recall that there are 10 \"Type1\" customers and 5 \"Type2\" customers. Assume the company cannot identify whether a particular customer is a Type1 or a Type2 customer. Derive the optimal twopart tariff scheme (assume a common usage price that is initially > MC). Moreover, explain why the access fees of Type1 customers are intertwined with the access fee of Type2 customers. \"Derive\" your answers by showing all steps / calculations and stating all assumptions. [10 Points] Calculate the optimal twopart tariff of \"cold\" and \"hot\" season CocaCola customers given that CocaCola that CocaCola @ identify a particular customer's type (assume MC = 5): qc = 26.17 3.98Pc + 2.251}, + 2.60Ac 062.4,, + 9.585 + 0.99Y Assume this is the demand function of an individual customer where l q = quarterly quantity of syrup sold I P 2 real 1 if spring/ summer price of syrup I Y : real 1ncome l A : square root of quarterly real advertismg expenses l S = { 0 i f winter /fall Average Values of Variables IQ = 30.22 .5 = 22-72-13? = 12.96-E = 8.16. I; = 5.89 .74; = 5.28. 17 = 20.63 \"Derive\" your answers by showing all steps / calculations and stating all assumptions. [20 Points] Use the information in part (e) to calculate the optimal twopart tariff of \"cold\" and \"hot\" season CocaCola customers given that CocaCola cannot identify a particular customer's type. \"Derive\" your answers by showing all steps / calculations and stating all assumptions
