Kindly, answer the following attachments.this question is complete.

For each of the following scenarios, begin by assuming that all demand factors are set to their original values and Big Winner is charging $300 per room per night.

If average household income increases by 20%, from $50,000 to $60,000 per year, the quantity of rooms demanded at the Big Winner (falls OR rises) from (..........) rooms per night to (.........) rooms per night. Therefore, the income elasticity of demand is ( positive OR negative ) , meaning that hotel rooms at the Big Winner are ( an inferior good OR an normal good)

If the price of an airline ticket from SFO to LAS were to increase by 10%, from $200 to $220 roundtrip, while all other demand factors remain at their initial values, the quantity of rooms demanded at the Big Winner (falls OR rises)from (..........) rooms per night to (.........) rooms per night. Because the cross-price elasticity of demand is ( positive OR negative ) , hotel rooms at the Big Winner and airline trips between SFO and LAS are ( substitutes OR complement ).

Big Winner is debating decreasing the price of its rooms to $275 per night. Under the initial demand conditions, you can see that this would cause its total revenue to ( decrease OR increase ) Decreasing the price will always have this effect on revenue when Big Winner is operating on the ( elastic OR inelastic ).

(Production function) Condsider a representitive rm with a. production function which is ( i) twice continuously dierentiable; (ii) exhibits positive and diminishing marginal product and (iii) has constant return to scale: Y = F(K, L) (1) Given the capital rental price R and the wage to, and the good price P is normalized to 1, the rm can choose K and L to maximize its prot: 1}1{acF(K, L) RK 10L (2) Using (5.3.13), prove and interpret the following relation in words: Arn = Udxn - axn-1 . Obtain an alternative expression for the variance given in Example 5.3.1 b starting with 1 - 20 + 2K _ 2(1 - Uk) - (1 - U2K) Y2 = 12 K = 0, 1, n - 1 ((a 7 7 )2 K= n, n +1 . . .. on 5.4 Assume a uniform distribution of deaths over each year of age. Simplify [ (jimPxt* 1 / mixtiti/ ml) $1- (+1)/md for use in interpretation of (5.4.8). Consider an m-thly temporary life annuity-due that pays 1 per annum to a annuitant age x for y - x years. a. Express the current payment form of the actuarial present value of the above annuity as a sum of that for payments in the first year and for the remaining y - x - 1 years. b. Express the actuarial present value of payments in the first year in term of a(m) and B(m) under an assumption of the uniform distribution o deaths within each year of age. c. Find the form of the c(x) and d(x) expressions for a recursion relation for such an annuity and indicate a starting value. Using (5.4.10), derive alternative formulas to (5.4.17) and (5.4.18). Show that the annuity-immediate analogue for (5.4.6) is a(m) = ] ax + i(m) (1 + DA, - (1+ 1 ) A ( ] . and that under the assumption of a uniform distribution of deaths in each year of age, this becomes am) = s7 a, + (1 + i) 1 - a1 i (m) -Ax. Show that the annuity-immediate analogues for (5.4.7) are a(m) = 1 - (1 + i(") / m)Agn) (m) _ i (m) as A (m)