:Please help me answer the following questions.

18. Assume that a firm produces its product in a system described in the following production function and price data:

Q = 3X + 5Y + XY

PX = $3

PY = $6

where X and Y are two variable input factors employed in the production of Q.

a. What are the optimal input proportions for X and Y in this production system? Is this combination rate constant regardless of the output level?

b. Is it possible to express the cost function associated with the use of X and Y in the production of Q as Cost = PXX + PYY or Cost = 3X + 6Y? Using this, what is the maximum amount of output that can be produced with a budget of $1000?

c. How much will output increase if the budget rises to $1500?

d. Suppose that the firm is interested in producing 14777 units of output. How much X and Y will be used and what is the cost?

2. Companies A and 3 face the following interest rates: cm...\" W... a Euro [fixed rate} 5% 1% Australian dollars [floating rate) LIBOR+U.5% LIBOR+1% (a) Assuming that A wants to borrow in Euro at a fixed rate and B wants to borrow in Australian dollars at a floating rateI derive an upper bound for :I: that allows these companies to enter into a profitable swap agreement. [8] (b) Assume now that :t: = 6%. Explain under what conditions, Company A would be interested in entering a swap agreement with Company B. [4] (c) Under the above conditionsI and considering :I: = 6%. design a swap that is equally attractive to both companies arranged by a financial intermediary that makes a profit of [1.2% from these operations. [8] b) Using the method of undetermined coefficients, find the response of the output gap and inflation to an exogenous increase in 9: when prices are sticky and monetary policy follows the Taylor Rule above. To do this, guess that the solution for each variable is a linear function of the shock ge: Ut = Ay9: (Hint: follow the steps used in the problem set. Start by substituting the guesses, the monetary policy rule and the AR(1) process for 9, into the dynamic equations (13) and (14).) c) How, and why, does the response of GDP differ from the model with flexible prices? Do positive government spending shocks increase inflation? Provide economic intuition and (if you can) discuss the solution you found in part (b). d) In principle, could monetary policy fully stabilize the output gap and inflation after a government spending shock? (Hint: think about how the 3-equation setup above looks like the cases we studied in class)? Would there be any additional benefit from conducting optimal monetary policy under commitment? 8 Question 6 (10 points) This question is about the standard decentralized real business cycle model. You do not need to derive anything for this question and keep your answers clear and concise. a) Briefly explain the mechanisms through which TFP shocks affect output, con- sumption, hours worked and investment in the standard RBC model. How well does the model replicate the business cycle facts seen in the data? How would adding habits in consumption affect the dynamics of consumption and investment? b) Suppose you want to solve the model using computational methods. Explain one approach, the advantages of this method and the steps you would need to take.) The Costa Coffee Company (for short Costa) is anticipating a major expansion of Its franchised coffee outlets into Europe and African countries. The investment opportunities available to the company involve rates of return and initial investment amounts that differ because of differences in operating costs and consumer demand in the countries involved, The total investment (M) that Costa can undertake is constrained by the cost of capital (2), which is defined by the following function: 1=6+0.8 M The initial investment and rate of return for each country are listed below in order of decreasing rate of return. Country Initial Investment ($ millions) Rate of Return (6) South Africa 3.8 16.0 Kenya 1.3 15.0 France 2.4 13.0 Germany 3.1 11.0 Ethiopia 1.9 90 (A) Plot the investment supply function (represented by above-mentioned cost of capital equation) and the investment demand schedule (represented by the table above) on the graph below. (B) Determine the optimal level of investment and the corresponding cost of capital for the firm. Also indicate the countries in which Cost should invest. 18 16 14 Rate of 10 Return 0 3 5 6 7 9 10 11 12 13 14 Capital Investment (M) Page 5 of 7