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43. An entrepreneur is engaged in tree growing. He purchases a seedling for 4 dollars, incurs a cultivation cost flow at a rate of G(t) = 0.4t dollars per year during the life of a tree, and sells the tree at t= T for R(T) =4 + 8T -T' dollars. The market rate of interest is 0.20. Determine an optimal length for his cultivation period, T. Apply the appropriate second-order condition to verify that your solution is a maximum.33. Consider a two-person two-commodity, pure-exchange economy with paper money. The utility functions are U1 = 911912 and Us = 921927 . Consumer I has initial endowments of 30 units of Q1, 5 units of Q2, and 43 units of money; II has respective endowments of 20, 10, and 2. Each of the consumers desires to hold a money stock equal to one-fifth of the value of her initial commodity endowment. Determine equilibrium money prices for Q, and Q2. Show that the equilibrium prices would triple if the initial money stocks of I and II were increased to 129 and 6 respectively.26. Let the demand and cost functions of a multiplant monopolist be p = a - b(q, + q1), Ci = @191 + 81qi, and Ca = @292 + 82q; where all parameters are positive. Assume that an autonomous increase of demand increases the value of a, leaving the other parameters unchanged. Show that output will increase in both plants with a greater increase for the plant in which marginal cost is increasing less fast.39. Assume that there are two consumers and two commodities. Let the utility functions be U, = quqn and Ur = quqn with qu + qu =qi and qu + qn = qr. Show that Scitovsky contours are given by qiq = ( U, + /U2).23. Assume fifty years supply commodity Q at location I and fifty at location II. The cost of producing output q for the i" firm (in either location) is 0.5q7. The cost of transporting the commodity to the market from location I is 6 dollars per unit and from location II, 10 dollars per unit. Determine the aggregate supply function.40. Name the famous theory of economics, which analyses the situations involving two or more interacting decisions makers with competing and conflicting interests, which also has its application in the formulations of nuclear strategies, ethics and evolutionary theory : (a) Greater Fool Theory (b) Goodhart's Theory (c) Fisher Theory (d) Game Theory17. An entrepreneur uses two distinct production processes to produced two distinct goods, Q1 and Q2. The production function for each good is CES, and the entrepreneur obeys the equilibrium condition for each. Assume that Q, has a higher elasticity of substitution and a lower value for the parameter o than Q2. Determine the input price ratio at which the input use ratio would be the same for both goods. Which good would have the higher input ratio if the input price ratio were lower? Which would have the higher use ratio if the price ratio were higher?46. Select the correct statement/statements regarding Foreign Currency Convertible Bonds (FCCBs) using the code given below : 1. FCCBs are counted as part of the external debt. 2. They are usually used by the Indian companies to raise short-term loan in foreign currency. CODE : (a) Only 1 (b) Only 2 (c) Both I and 2 (d) Neither I nor 230. Let two duopsonists have production functions q, = 13x, - 0. 2x1 and q2 = 12x2 - 0. 1x; where x1, x, are the input levels employed by the duopsonists. Assume that the input supply function isr =2 + 0.1(x1 + x2) where r is the supply price of the input, and that qu and q are sold in competitive markets for prices pi =2 and p: =3. (a) Find the input reaction functions. (b) Determine the Cournot equilibrium values for x1, x2, and q1, q2, 1 1, 12
