19. Two individuals exist in a perfectly competitive market (the fact that only 2 individuals exist and we're calling the market perfectly competitive is a bit odd, but bear with me). The first 1 3 individual's preferences are of the form U1(x1,x2) = x1/4x2/4. He has an income of $12. 1 1 The second individual's preferences are of the form U1(x1,x2) = xl/sz 2. Her income is $16. Two firms also exist in the market. They produce Good 1. The first firm's production 1 1 technology for Good 1 is of the form x1 = fl ("(11,112) = 711/2 + 712/2 (where n is a necessary input good). The second firm's production technology is a Cobb-Douglas of the 1/ 1/ form 361 = f2 (111,112) = H1 4112 4. The costs of the input goods are both $1. What is the perfectly competitive equilibrium price for Good 1? Hint: Solve the for each firm's cost ECON 30010: Intermediate Microeconomic Theory 3W7, Cronin function. Then, figure out how much each firm will supply by maximizing their PC profit function. Then, determine how much each individual will demand by solving the Consumer's problem. Last, find the price that sets market supply equal to market demand