Please help me answer the following questions.,,,

3 The pension scheme of a certain company provides an annual pension on retirement (for 'age' or 'ill- health' reasons) of amount equal to one per cent of the member's total earnings throughout his service. The pension is payable weekly. In addition, in the event of a member dying in service there is payable at the time of death a lump sum of 30,000. There is no benefit on withdrawal. The company pays a constant percentage of all the members' salaries into the pension fund. The percentage is that which will exactly cover the cost of benefits for a new entrant to the fund at age 30 with an initial salary rate of f10,000 per annum. Contributions are payable continuously, and the employees do not contribute to the scheme. Expenses are negligible. (a) Calculate the contribution rate paid by the company, assuming the last retirement age is 65. (b) A valuation of the fund is to be conducted. For each active member of the scheme there is recorded(i) the age nearest birthday (which is regarded as the member's exact age) at the valuation date, (ii) the annual salary rate at the valuation date, and (iii) the total past earnings in service (prior to the valuation date.) For each age, the totals of (ii) and (iii) are recorded and the following is an extract from the data. Age r No. of members Total past earnings Total of annual salary aged x for members aged r rates for members aged r 25 11 302,100 70,100 Assuming that the basis of the Tables provided is appropriate, find the liability at the valuation date for the benefits payable to the members aged 25, and determine whether the future contributions payable in respect of these members are more or less than sufficient to cover the benefits. 4 A pension scheme provides each member who retires (for any reason) with annual pension equal to x final salary per year of service. Final salary is the average income over the last 3 years of service, and fractions of a year of service are not included when calculating the pension. Assuming that equal contributions are payable by the member and his employer, that in the event of death in service a benefit is payable equal to the return without interest of both the member's and the employer's contributions, and that in the event of withdrawal from service a return without interest is made of the member's contributions, calculate the appropriate contribution rate payable by both the member and his employer in respect of a new entrant aged 40.1. Assume that the market for steel is competitive. The inverse demand curve for steel 13 P 12ll Q and its inverse supply (i. e. ,industry marginal cost] curve is P: Q + 20, where P is price and Q 15 quantity. (3} Depict these inverse demand and supply curves in a diagram and use algebra to calculate the market equilibritun values of price, Po, quantity, QC, and price elasticity of demand, EC. [ll]I points] (1)) In the above context, also calculate consumer surplus, CSC, producer surplus, PSE, and social welfare, SW}. [10 points] 2. Suppose that the industry in Question 1 is taken over by a monopolist. (a) Depict the monopolist's prot maximization problem in a diagram and use algebra to solve for the values of price, Pm, quantity Q1], and price elasticity of demand, Em. [ll]| points] (b) Calculate the impacts of monopolization in terms of the resulting changes in consumer surplus, producer surplus, and social welfare. [10 points] 3. (a) Return to the scenario in Question 1 and assume that the process of producing steel causes air and water pollution, which result in marginal external cost NIEC = 21']. Taking this extemality into consideration, calculate the socially optimal level of steel production, Q5, and illustrate its determination in a diagram like the one for Question 1(a) by using any additional curve that may be needed. Also calculate social welfare, SW5. [ll] points] (b) If the competitive market fails to account for external costs and continues to produce at Q: {'om Question 1(a)), what would be the resulting loss in social welfare? Explain your calculation with the help of a diagram. [5 points] (c) Calculate a per unit tax that could correct the market failure in part (b). If this tax is implemented, what would be the resulting values of social welfare, consumer surplus, producer surplus, total external costs, and total tax revenue? Also illustrate these areas in a diagram. [15 points] Question 1 (total 15 points). A firm has a production function: f(K, L) = 50LK0-5 + 12 K2 - 13K3 a. What is its short-run production function if capital is fixed at K=4? b. What are the firm's marginal product of labour and average product of labour in the short run? c. Calculate the elasticity of output with respect to labour. Question 2 (total 16 points) . Do the following functions exhibit increasing, constant, or decreasing returns to scale? Explain your answers. a. The production function O = 1050-5105, where M is materials, K is capital and L is labour. b. q =L +0.5K c. q = 0.5LK'0.25 d. q=417 +4K Question 3 (12 points). Find the Marginal Rate of Technical Substitution for the following production functions: a. q= DKi b. q =L0.5 + K0.5 c. q =L+K Question 4 (Total 10 points). Suppose a firm's cost function is C = 2q' - 16q2 + 90q, average cost curve is described by the equation AC=2q- - 16q + 90. At what output level does the marginal cost curve cross the average cost curve? Question 5. (16 points, 8 points each) For the following, please answer "True" or "False" and explain why. a. When buying a piece of equipment, it is always best for the firm to pay cash instead of borrowing the funds since this renders the equipment less costly. b. University of Toronto is choosing a location for a new building. The university has campuses at Downtown, Scarborough and Mississauga. A large parcel of land would have to be purchased at Scarborough or Mississauga if the building were to -Page I- be built there. So it is cost-effective to locate the new building at downtown because the university already owns the land