Solve the problems as attached below.
1) Suppose that Lisa consumes two goods, bread (represented by x) and cheese (represented by y). Suppose that your utility function is: U(x.y) = xy 4 [1]. Assume the time period is I week. The marginal utility functons for bread and cheese are respectively: MU,(x,y) =()" [2] and MU,(x,y) = ()" [3] a) Find the equations of 3 of Lisa's indifference curves (IC) for which the value of utility is held constant at respectively U = 10,U = 25, and U = 50. b) In Table 1, for each IC, plot the y values corresponding to the x-values. Now, use the table values to plot each of the three ICs on Fig. 1 (see table and graph grid at end of the assignment). On your graph, draw an arrow to indicate the direction of increasing utility. c) Use the functions [2] and [3] to find the equation of the marginal rate of substitution (MRS) in terms of the amount of the y-goods Lisa is willing to give up to get an additional "small unit" of x-goods. Le. the rate at which Lisa is willing to exchange y-goods for x-goods starting at a given bundle (x.y). Note: We can think of this MRS as Lisa's marginal benefit (MB) of bread measured in units of cheeses. d) On the IC at which O = 25, label the bundle A = (25. 25) and draw a tangent line and use the formula, MRS(x.y) = - slope tangent at the bundle = - (rise)run. Repeat for two other spaced out points on the IC [one to the right of A (call it B) and one to the left of A (call it C)]. e) Suppose that Lisa's weekly food budget is M = $100 and the price of bread (p,) is $1/unit while the price of cheese is py = $3/unit. Write down an equation for Lisa's budget line and rearrange it to get y as a function of x. Plot your budget line on Fig. I and label it. Also, label Lisa's feasible and non-feasible sets of consumption bundles by light shading in different colours.Minnie consumes two goods. I. and .tg and her utilityr function is it = [I] + 2:}(172 +4) a} {5 points} Find her Marshall demands \"(pl \"113, m) andxpl ,pg, m) using the Lagrangian function. h} [3 points} Express the indirect utility function v(p1.p2, m) and simplify the expression. c} {3 points} Derive the expenditure function 071,132, it) from indirect utility funcon. d} [3 points) Derive the Hicksian demands it 1 (p; , pg, 11) and 13031 1p: , it) using the Shepherd's lemme. e} [6 points} Assume that Minnie's budget is $120 and x1 costs $10 while .172 costs $5. Now suppose that the price of :2 increases to $20. calculate the substitution and income effect due to this price change for both commodities using the Hicksian decomposition. fect. Please see the preface for more information. Basic Problems 1. You invest $3,000 for three years at 12 percent. Fu What is the value of your investment after one year? Multiply $3,000 x 1.12. (L What is the value of your investment after two years? Multiply your answer well to part a by 1.12. What is the value of your investment after three years? Multiply your answer to part b by 1.12. This gives your final answer. d. Combine these steps using the formula FV = PV x (1 + 0)" to find the future Jo eu value of $3,000 in three years at 12 percent interest. 2. What is the present value of a. $7,900 in 10 years at 11 percent? b. $16,600 in 5 years at 9 percent? c. $26,000 in 14 years at 6 percent? 3. a. What is the present value of $140,000 to be received after 30 years with a 14 percent discount rate? b. Would the present value of the funds in part a be enough to buy a $2,900 concert ticket?7 Outline the process used by futures exchanges to remove the credit risk of individual participants. [2] Table I below shows part of the operation of a margin account for a short position in two gold futures contracts. The initial margin is US$2,000 per contract and each contract is for delivery of 100 ounces of gold. The closing futures prices are in USS per ounce of gold. Copy the table into your answer book and fill in the entries in the blank columns. Table 1 Operation of the margin account for two gold futures contracts. Date Closing Daily Gain Cumulative Margin Futures (Loss) Gain (Loss) Account Price Balance US USS USS USS Futures price at which contract is entered into on: May 3rd 400 May 3rd 396-5 May 4th 399 4 May 5th 400.4 May 6th 399 7 May 7th 405.9 May 8th 397.9 [6] (ili) Describe briefly two major differences between the trading of currency futures contracts on an exchange and the trading of forward currency contracts in the Over-the-Counter (OTC) market. [2] [Total 10] Write down a formula for the after tax return for an investment whose dividend is d and capital gain is g- [1] State any assumptions that you have made in this formula. (iii) Describe what other factors an individual will need to take into account in practice to determine his after tax return. [3]
