Liam is an owner of a collection of Roman and Greek coinage that is worth $20 (in million). Liam is planning to participate in the 2020 Coin Show. This exposes him to the risk of potential theft. The probability of theft is substantial, w=; It follows that the collection is a lottery w = (wt, wnt) = (0, 20). Liam's Bernouli utility function is u(c) = 10 Inc. a) Write down Liam's Von Neumann-Morgenstern (expected) utility function over lotteries U(Ct, C nt) (give a formula). (10 pts) b) Liam can insure against theft by paying premium y = . What are the implicit prices of wealth in the event of theft, p, and in no-theft pm? (two numbers). (10 pts) c) Write down two secrets of happiness, find optimal level of wealth (Ct, Cast) and coverage I. (three numbers) Is Liam going to fully insure (yes-no answer and one sentence)? (12 pts)Problem 2. (Producers) (32 pts) Consider production function given by F(K, L) = 3X414. a) Using the A argument demonstrate that production function exhibits decreasing returns to scale. (10 pts) b) Derive the cost function given PK=PL =9. (10 pts) c) Find the MES point of the fixed cost F=8 (12 pts)If we graph Mary's indifference Curves with avocados on the horizontal axis and grapefruits on life vertical axis, then whenever she has more grapefruits than avocados, the slope of her indifference curve is -2. Whenever she has more avocados than grapefruits, the slope is -1/2. Mary would be indifferent between a bundle with 22 avocados and 37 grapefruits and another bundle that has 37 avocados and (a) 27 grapefruits. (b) 32 grapefruits. (c) 17 grapefruits. (d) 22 grapefruits