give clear and precise solutions with sources

During a pandemic, each industry has a representative competitive firm whose output sells for a unit price of $1 and has the linear production function AL(1 I) where L is there total number of employees and I is the share of employees who are sick. Employees can get sick at work or during leisure so that I = Iw + Il and each employee earns a wage w independent of their health status. The firm can exert social distancing effort a at cost c(a,L) = 21a2L and the share of people infected at workisIw =(1a).

(a) The model assumes that employees earn a full wage independent of their health status. In one or two sentences, describe a realistic government regulation that would make this assumption reasonable.

(b) Write the firm's profit in terms of A,L,Il,,a and w.

(c) Find the firm's optimal choice of a as a function of parameters.

Now consider L workers who choose amounts of consumption c and non-home leisure l. If a worker is sick they receive disutility so that a representative agent has preferences over consumption, non-home leisure, and the share of people infected and chooses

max c+ l(Iw+Il)s.t.c=wT

c,l where the utility function is u(c, l) = c + l (Iw + Il), w is the wage (paid

by the firm), T is taxes paid, and the non-workplace infection rate is given by the

function Il = (l) l, a linear function whose slope increases in the average amount

of non-home leisure l. (d) Find an individual's optimal choice of l as a function of parameters assuming

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they do not account for their effect on infection rates (that is, assume l, and T

are exogenous to the agent's problem).

Hint: Substitute constraints Il = l(l) and c = w T to get a one-variable maximization problem.

(e) Write out (but do not solve) the problem of a benevolent social planner who chooses c,l, and a to maximize the agent's utility subject to the constraint that total consumption cannot exceed the difference between firm profit and healthcare costs (Iw + Il)L.

(f) In the competitive equilibrium all agents make the same choices so that l = l and competitive leisure and abatement choices are not efficient. Explain the source of the inefficiency and whether each of l and a are too big or too small in the competitive equilibrium.

Take a close look at the SPP derived in (e) and compare with the firm's profit and household's utility maximized in parts (b) and (d), what's missing from (b) and (d)?

There are two types of consumers: one half of consumers are type 1 (low type) and the other half are type 2 (high type). Type 1's demand curve is q1 = 4 P, while type 2's demand is given by q2 = 6 P. Consider a monopolist selling its product to these consumers. Assume that the marginal cost is equal to zero.

However, the firm does not know an individual consumer's type. It only knows that there are two types of consumers with demand curves given as above. Suppose that the firm can offer only a single two-part tariff, (T,P), where T is the lump-sum fee and P is the unit price.

(1) If the firm serves only high type consumers, what should be the optimal two-part tariff, T and P ? Also, compute the resulting profit.

(2) If the firm serves both types of consumers, what is the firm's profit when it offers (T,P)? Find the expression in terms of P only.

(3) Compute P that maximizes the firm's profit in (2). Also, compute the optimal T, as well as the resulting profit.

(4) Compare the profit from (1) and the profit from (3), and determine which two-part tariff will be chosen by the firm. Also, compute the social surplus from the two-part tariff chosen by the firm.

Suppose there are only two investment alternatives: a bank deposit that pays 4% per year, and a 2-year coupon bond with face value of $1,000 and 9% annual coupon rate. Assume bank deposit and the coupon bond are perfect substitutes. (For all the calculation, please make sure to show all formulas and round the values to 2 decimal places.)

a) Calculate Pi - the market price of the bond at the beginning of year 1.

b) Calculate P: - the market price of the bond at the beginning of year 2.

c) What is the ex-ante (expected) annual rate of return for year 1? What is the ex-ante annual rate of return for year 2? Assume now that at the beginning of year 2, the deposit interest rate unexpectedly rises to 12% annual.

d) Calculate P2*- the new bond price for year 2.

e) Calculate RET1 - the ex-post (realized) rate of return on the bond in year 1.

f) Calculate RET- the ex-post rate of return on the bond in year 2

Exercise 2 The Jambon Factory checks the performance of its carriers each quarter by looking at different evaluation categories (scorecards). The Jambon Factory sends a report called "Rating Report" about its carriers' performance to its traffic department at the end of each quarter. The specific report shown below corresponds to the Quarter 4 20XX for the following less-than-truckload carrier: Jean Marteau (ID: 67859). A carrier has an ID, a name, an address, and can be categorized as truckload or less-than-truckload.

Draw an ERD reflecting the data contained in the Rating Report. A scorecard has a code (e.g. SAF238) and a name. Any scorecard for a certain carrier at a certain date, displays the score the Source attributed to that carrier at that time. Assume that each scorecard is provided by one external source only. A source can provide several types of scorecards. A source has a name (e.g., SAFER or FMCSA), a HQ address, and an authority level. The authority level of the sources can be "Federal" or "State".

Explain what you chose for the identifier of each entity type on your ERD.

A. An analyst was asked to predict the gross social benefits of building a public swimming pool in LGA, which has a population of 80,000 people and a median household income of $42,500. The analyst identified 24 towns in the region that already had public swimming pools. They conducted a telephone interview with the recreation department in each town to find out what fee it charged per visit (FEE) and how many visits it had during the most recent summer season (VISITS). In addition, they were able to find each town's population (POP) and median household income (INCOME) in the most recent census. Based on the obtained data they were able to identify the following relationship

VISITS = 140000 - 14638*FEE -0.001129*INCOME + 0.7551*POP

i. What is the gross benefit of opening a public swimming pool in LGA and allowing free admission? [4 marks]

ii. Estimate the loss in gross benefits if admission fee is set at $2.00. [4 marks]

B. Why do we need to consider shadow price during CBA? [2 marks]