. Solve these questions please.

(.5) (i) for is the forward rate applicable over the period t to t + r. it is the spot rate over the period 0 to t. The gross redemption yield from a one year bond with a 6% annual coupon is 6% per annum effective; the gross redemption yield from a two year bond with a 6% annual coupon is 6.3% per annum effective; and the gross redemption yield from a three year bond with a 6% annual coupon is 6.6% per annum effective. All the bonds are redeemed at par and are exactly one year from the next coupon payment. (a) Calculate i, i and i; assuming no arbitrage. (5) (b) Calculate 6,1 , fi,1 and f 2, 1 assuming no arbitrage. (5) (ii) Explain why the forward rates increase more rapidly with term than the spot rates. (2) (iii) You are given the following term structure of spot interest rates: Term (in years) Spot interest rate 5.00% 2 5.75% 6.25% 6.50% A three-year annuity- immediate will be issued a year from now with annual payments of Rs.5000/-. Using the forward rates, calculate the present value of this annuity a year from now. (3) [15]A. professional gambler has said: \"Flipping a coin into 1e air is fair, since the coin rotates about a horizontal axis, and it is equally likely to be either way up when it rst clips the ground. So a flicked coin is equally likely to land showing heads or tails. However, squirming a coin on a table is not fair, since the coin rotates about a vertical axis, and there is a systematic bias causing it to tilt towards the side where the embossed pattern is heavier. In fa:t, when a new coin is spun, it is more than twice as likely to land showing tails as it is to land showing heais." After hearing this, you carried out an experiment, spinning a new coin 25 times on a polished table, and found that it showed tails 13 times. Do the results of your experiment support the gambler's claims about the probabilities when a coin is spun? [3] expenditure. Consider an economy characterized by the following 13 equations: ng61b C = 500 + 0.75Y + 0.05W I = 150 where C is desired consumption, I is desired invest- ment, W is household wealth, and Y is national income. a. Suppose wealth is constant at W = 10 000. Draw the aggregate expenditure function on a scale diagram along with the 45 line. What is the equi- librium level of national income? b. What is the marginal propensity to spend in this economy? c. What is the value of the simple multiplier? d. Using your answer from part (c), what would be the change in equilibrium national income if desired investment increased to 250? Show this in your diagram. e. Begin with the new equilibrium level of national income from part (d). Now suppose household wealth increases from 10 000 to 15 000. What happens to the AE function and by how much does national income change?Please refer to the background information below to answer the following six questions. Two firms, X and Y, have access to seven different production processes, each one of which has a different cost (dollars) and gives off a different amount of pollution (tons). The information is summarized in the table below. Process (daily smoke) Cost to Firm X Cost to Firm Y A (6 tons) 80 330 B (5 tons 210 720 C (4 tons) 420 1180 D (3 tons) 710 1750 E (2 tons 1080 2450 F (1 tons) 1530 3380 G (0 tons 2080 4480 23. If pollution is unregulated, and negotiation between the firms and their victims is impossible, firm X will use the production process [ Answer23A ], firm Y will use the production process [ Answer23B , and the total smoke emitted will be [ Answer23C ] tons per day. 24. Suppose the city council set a tax of 295 dollars on each ton of smoke emitted each day. We would expect the firms will emit a total of [ Answer24 ] tons of smoke per day. 25. Suppose initially there is no regulation on pollution (in particular, no tax is imposed on pollution), and the city council has recently decided to cut the total pollution (smoke emissions) by half. If the city council requires each firm to cut its emission by half, the total cost of reducing the emssion to the society will be [ Answer25 ] dollars per day. 26. Continue to assume that the city council wants to cut total smoke emissions by half. Suppose the city council like to set a tax of T dollars on each ton of smoke emitted each day. To achieve the desired reduction in emission, the T should be more than [ Answer26A ] and less than [ Answer26B ]. 27. Continue from the previous question. Using tax as a tool, the total cost of reducing the emission to the society is [ Answer27 ] dollars per day. 28. From the society's perspective, to cut the emission by half, it would be optimal for firm X to adopt process [ Answer28A ] and firm Y to adopt process [ Answer28B ]