Instructions: Show all of your work!!!! Upload photos or scanned pdfs of your work using the submission link provided. 1. Calculate the expected profits for each of the following scenarios: a. Thereis a 0.25 probability that you have profits of 10, a 0.40 probability that you have profits of 15, and a 0.35 probability that your profits are 20. b. You produce 100 units at a cost of $20 each, but you are uncertain about the price you will receive for your goods. The price you will receive is either $15 or $30, each having equal probability. 2. Calculate the profit-maximizing level of output for a perfectly competitive firm in each of the following circumstances: a. The firm's cost function is given by c(Q) = % Q?, and the price = $10 with probability %, and equals $30 otherwise. b. The firm's cost function is given by c(Q) = iQ'-, and the price equals $6, $9, or 515, each with equal probability. 3. Consider the production function Q = 10L %Lz + 24K K?, where L is labor and K is capital. Suppose the input prices are $40 for labor and $80 for capital and the price of output is $10. a. Suppose in the example above, you find that the firm is producing using five units of labor and five units of capital. What advice would you give them regarding changing their input mix? More labor intensive or more capital intensive? How do you know? b. Solve for the optimal input mix for this firm. 4. Consider the production function Q=2L-{1/2)L2+2LK+4K-(1/3)K? where L is labor and K is capital. Suppose the input prices are $1,000 for labor and $1,500 for capital and the price of output is $100. Determine the optimal quantity of each input