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Problem 1: Consider the reference desk of a college library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 17 requests per hour can be used to describe the arrival pattern and the service times follow an exponential probability distribution with a service rate of 20 requests per hour. a. What is the average number in line waiting to be served? b. What is the average time that a patron must wait to get through the system? C. What is the utilization of the librarian? d. What is the probability that when you arrive there will be three or more patrons ahead of you?Reserve Requirement = 20% 1. The Fed buys $550 million in bonds and deposits it at HCC Bank of Students. "What is the value of required reserves? How much can the bank lend out (or in other words, what is the value of excess reserves)? 2. HCC Bank of Students loans out the entire amount of excess reserves from problem 1 above to a student, C. Ash C. Ash, takes this money and deposits it at Wells Fargo Bank. -What is the value of required reserves? "How much can the bank lend out (or in other words, what is the value of excess reserves)?4. After the pandemic is over, the loss of government revenue due to the economic lockdown and the cost of the worker compensation scheme, made government debt soar and the treasury asks you for advice on how to reduce government debt. a) Currently, the citizens of Korona pay a flat tax on labour income of 20% and a proposal by the minister is to increase the tax rate to 30% if income exceeds the threshold of $20,000. Give your assessment of the likely effect of the proposal on labour supply, paying particular attention to the underlying forces at work. Briefly comment on how these forces may affect government revenue. [You can include a graph if it helps to illustrate your reasoning; word limit 250 words; 8 marks]. b) An alternative policy proposes to introduce a tax on inheritances to raise the same amount. Assess the effect on welfare of this inheritance tax allowing for different behavioural responses. [word limit 200 words; 6 marks]. c) Contrast the proposals in a) and b) regarding the potential for off-shore tax evasion. [word limit 200 words; 6 marks].EXERCISE 3 A firm's production function is f(T1, T2) = CT2 . The prices of inputs 1 and 2 are both $1. (1) If x2 is fixed at 2 in the short run, derive the firm's short-run cost function cs(y) and the firm's short-run supply function Q s(p). Compute short-run producer surplus for p=10. (2) Derive the firm's long-run cost function c(y) and the firm's long-run supply function Q(p). Compute long-run producer surplus for p = 10.2. Currently, Krona has currently no compensation scheme for workers infected with the disease and you are advising the government on the introduction of such a scheme (suppose for this exercise that there are no other unemployment or sick benefits and this would most likely concern any future disease). Model the economy with identical individuals who earn a wage of 500 while working and 0 when sick with the disease. With probability q, the individuals get sick with the disease and cannot work. When sick, individuals would receive a sickness compensation s from the government. To finance the scheme, when working individuals pay lax of (500*t) where t is the tax rate. u(c) = c1/$ denotes the individuals utility from consumption of c in any given state. a) Write down the individual's expected utility as function of s, q and t. [3 marks] b) What is the government's budget constraint for an actuarially fair compensation scheme; write down what is balanced government budget in terms of s, q and t. [2 marks] c) Find the value of compensation s that maximizes individuals expected utility, assuming a balanced budget. [6 marks] d) What is the tax rate t required to finance the compensation maintaining a balanced budget? Discuss very briefly the intuition (2 sentences). [4 marks] e) Discuss briefly the merits of the introduction of such a disease specific compensation scheme, including a brief discussion of moral hazard. [5 marks]