tackle the following with a thorough explanation......

1 Short Answer Questions 1. The price eluticity of demand for gasoline is -2%%. If the government wants to reduce gasoline consumption by 20%% how much should it increase the price of gasoline? 2. The cross-price elasticity of good z as a consequence of an increase in the price of good y is-0.5. Are goods r and y substitutes or complements? 1. Suppose that 2 identical firms produce the same good at marginal cost e and they compete a la Bertrand. Draw the best response of Firm 1. 4. When do we say that a firm has market power? Can you name two sources of market power? 5. Suppose that the elasticity of demand for cars in Germany is -2 and -3 in the U.K., while the marginal cost of these curs is $20,100. How will prices differ in Germany and the U.K.. 2 Monopoly, Cournot and Stackelberg KEY - The market demand function for gelato in Summersville is Its east function for producing gelato is TC - 5 + 209. 1. What is fixed cast, the variable costs, average costs and marginal costs of producing gelato? Does the cost function of gelato have economics or diseconomies of scale?" 2. Suppose that there is only ONE producer of bathing suits. Find the profit-maximizing quantity and price for bathing suits. 1. Suppose that firm can perfectly price discriminate (first degree price discrimination). How much will is produce? How much will its profits be? 4. What will be the equilibrium prices and quantities, if there are TWO firms that choose quantities simultaneously? (Cournot Competition)- 5. Now assume that the first firm gets to choose quantity before the entrant. What are the quan- tities that these firms will produce and the price in the market (Stackelberg Competition). Why are those quantities different?Problem 2: Consider a single-server queue with infinite buffer space (a) Consider the situation . The inter-arrival time is a constant and is given by 1 sec . The service time required by each customer is always 0.5 sec 2 What is the mean waiting time per customer? (b) Consider the situation . The inter-arrival time is exponentially distributed with mean 1 sec . The service time required by each customer is exponentially distributed with mean 0.5 sec What is the mean waiting time per customer? (c) Compare the answers of (a) and (b), what conclusions can you draw?Example 6 For a small batch computing system the processing time per job is exponen- Lially distributed with an average time of & minutes. Jobs arrive randomly at an average rate of one job every 4 minutes and are processed on a first-come-first-served basis. The manager of the installation has the following concerns. (a) What is the probability that an arriving job will require more than 20 minutes to be processed (the job turn-around time exceeds 20 minutes)? (b) A queue of jobs waiting to be processed will form, occasionally. What is the average number of jobs waiting in this queue? () It is decided that, when the work load increases to the level such that the average time in the system reaches 20 minutes, the computer system capacity will be increased. What is the average arrival rate of jobs per hour at which this will occur? What is the percentage increase over the present job load? What is the average number of jobs in the system at this time? (d) Suppose the criterion for upgrading the computer capacity is that not more than 10% of all jobs have a time in the system (turn-around time) erecting 40 minutes. At the arrival rate at which this criterion is reached, what is the average number of jobs waiting to be processed?Example 7 A computing facility has a large computer dedicated to a certain type of on-line application for users who are scattered about the country. The arrival pattern of requests to the central machine is random (Poisson), and the service time provided is random (exponential) also, so the system is an M/M/1 queueing system. A proposal is made that the workload be divided equally among n smaller machines - each with 1 times the processing power of the original machine. It is claimed that the response time (time a request is in the system) will not change but the users will have a local computer. Are these claims justified?1. Human Capital in the Solow-Swan Model: Suppose that the production function in the Solow-Swan model is given by Y(t) = AK(t)"H(t)L(t) 1-a-x where Y is output, A is technology, K is physical capital, H is human capital, and L is labour. Assume that 0 So 0. Output can be converted one-to-one into either investment in physical capital or human capital. Saving directed towards investment into physical capital is given by 0