_Help me answer this Macroeonomic problem.
(C) If shovels rent for $5, and workers must be paid $25, draw several isocost lines. (D) If BBQ-Yee32l has received a state contract to ll 30 potholes, what is the minimum cost at which it can fulll the contract? (E) If the cost of renting a shovel suddenly rises from $5 to $6, what will happen to the composition of inputs that BBQ-Yee321 uses to ll potholes? Why? Aside from catering for outdoor parties, BBQ-Yee32l also x potholes in Bloomington. BBQ-Yee32l's road crews ll potholes using workers and shovels in 1 to 1 correspondence. A worker with 1 shovel can ll 10 potholes in a day. A worker with 2 shovels can still only ll 10 potholes, as can 2 workers with 1 shovel. (A) Draw the production isoquant corresponding to lling 30 potholes. (B) Assume that production displays constant returns to scale, and draw a few more iso- quants. Question 2 {Production Functions and Growth Accounting}. Suppose an economy is characterized by the aggregate production function 1r\"; = F[K, Lt} where H is total output, Kt is the capital input, and L1 is the labor input, or number of workers. a] If the production function takes the constant elasticity of substitution {GEE} form given by F{Kt, L1} = 14(ng + [1 oc]LU% where A 3:- {1,41- E [I], 1}, and 1" dz: 1, show that both marginal products are positive and decreasing. b] For the CES production function above, show that there are constant returns to scale. c] It can be shown that the CES production function approaches the CobbDouglas pro duction function F[K._,Lt} = Alifill\" as r 3- I]. Find the wage rate and the rental rate of capital under the assumption that inputs are chosen to maximize prots. d] With the CobbDouglas production function ab ove, write down the growth rate of total output Y, as a function of the growth rates of capital 3g and labor a. e) Under the assumptions of the Solow growth model with Cobb-Douglas production, write down the growth rate of consumption per capita as a function of g}; and n. Consider a binomial tree model for the non-dividend paying stock with price S, Assume this price either rises by 30% or falls by 20% each quarter (3 months) for the next three quarters. Assume also that the risk-free rate is 2% per annum continuously compounded. Let So = 160. (i) Calculate the price of a vanilla European call option with maturity in nine months* time and a strike price of $55. [3] (ii) Calculate the price of a vanilla European put option with the same maturity and strike price as the contract in part (i). [1] Assume the investor has a portfolio formed by a short position in the call option given in part (i) and a long position in the put option given in part (ii). (iii) Determine how the value of the portfolio would differ if the possible change in the stock price was a fall of 30% instead of 20%. [3]
