can I get help on these questions listed below ?

E&M201 Final Exam Spring 2021 Answer all questions. Please show all your work and label all your diagrams carefully and completely to get full credit. 1. (10 points) For each of the following production functions, find out whether it has increasing, decreasing or constant return to scale. a. f(L,K) = L1/SK2/5 b. (L,K) = 3L + K 2. (20 points) Assume that a firm in a monopolistic market sells a product with a total cost function TC=2000+0.503 and a marginal cost function MC=Q. The market demand curve is given by the equation P=200-0.5Q. a. Calculate the profit maximizing Q", P*, and the profit. Graph the demand, MR, MC, and ATC. Mark Q", P*, ATC* (you'll have to calculate the values). b. Calculate the deadweight loss that occurs in this market because it is a monopoly instead of perfect competition. 3. (10 points) Suppose both automobile and book markets are monopolized. An automobile market has the demand elasticity is -2 while a book market's demand elasticity is -0.5. For both markets, MC is fixed at $25. Which market has a higher mark-up? Explain (Lerner Index: (P-MC)/P = - 1/Ed). 4. (30 points) A competitive firm's total cost function is TC = 503 + 40, fixed sunk costs are $20, and MC = 10Q. There are 100 firms in the market, and the market demand is given as P = 60 - 0.5Q. a. Find an individual firm's supply function. b. Calculate the profit maximizing q*, P*, and the profit of an individual firm. 5. (20 points) Billy's income is equal to I=100 and his utility function is U = 1. There is a 10% chance that he will be in an accident next year with his skateboard that will cause $70 worth of damage. a. Risk premium = Expected Value - Guaranteed income. Get the risk premium for Billy. b. An insurance company offers a policy that will cover all the damages if an accident occurs. Calculate the fair price for the insurance (Fair price = Good outcome - Expected Value). 6. (10 points) Below are the willing prices for buyers and sellers in a used-car market. Assume that buyers believe that 30% of cars are Lemons and 70% are Plums. How much are they willing to pay? If a buyers suggest their willing price, which cars will be sold? Plum Lemon Buyer's Highest $2400 $1200 Willing Price Seller's Lowest Willing Price $2000 $1000