r .NET.\rat the optimal choice is u = 0. The optimal choice of x occurs where price,\r1, equals marginal cost, x, so x = 1. At this point the worker gets a utility of\rx + K c(x)=l+K 1/2=1 /2+K. Since the worker's utility must equal 0, it\rfollows that K = 1/2.\r4. Given the setup of the previous problem, what would the worker be\rwilling to pay to rent the production technology\r. We saw in the last answer that the prots at the optimal level of production\rare 1/2. Since u = 0, the worker would be willing to pay 1/2 to rent the\rtechnology.\r5. How would your answer to the last problem change if the worker's\ralter- native employment gave him u= 1\r. If the worker is to achieve a utility level of 1, the rm would have to give\rthe worker a lump-sum payment of 1/2.