Devlin-Mcgregor hires labor to produce Soma. If L is the amount of labor used in the production of Soma, the quantity of Soma produced will be f(L) = VL. There are 2 agents Alice (A) and Bob (B) in the economy, who have one unit of free time and consume Soma. They each own half shares in Devlin-McGregor's profits. They also have identical preferences represented by the utility function u(x, l) = x2(1 l), where x is the number of units of Soma consumed and l is the number of units of labor supplied. Let labor be the numeraire so that the wage per unit of labor, denoted w, is 1. Denote the unit price of Soma by p. = = 1. Determine the profit maximizing level of labor that Devlin-McGregor should acquire as well as the profit maximizing quantity of Soma as a function of p and the wage. 2. Determine the utility maximizing quantity of Soma purchased by Alice as well as the amount of labor supplied by her as a function of p and the wage. 3. What is the Walrasian equilibrium price and allocation? 4. Alice and Bob together invent an improved technology for producing Soma. This is reflected in the production function of the new technology denoted g(L) = 2VL. Devlin-McGregor is considering purchasing this technology at a price of $3.20, which Alice and Bob will divide in half. Assume the prices stay at the equilibrium level identified in part (3), is it profitable for Devlin-McGregor to purchase and deploy the new technology? 5. A consultant argues that this is not the right way to decide whether to purchase the technol- ogy. The new technology will change the equilibrium price and allocations, and consequently Devlin-McGregor should compare the profits at the new price level to the original profit. Devlin-McGregor's CEO, however, says it would lead to the same conclusion. Determine which of the consultant or CEO is correct