Let's consider the economic impact of the pandemic on the economy. Assume that the pandemic evolves...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let's consider the economic impact of the pandemic on the economy. Assume that the pandemic evolves according to the basic SIR model: S i R and = = = -BS(t)I(t) BS(t)I(t)-I(t) yI (t) with initial conditions S(0), I(0), and R(0), satisfying S(0)+1(0) +R(0) = 1 S+I+R=0= S(t) + I(t) +R(t) = 1 for all t > 0. Assume that some fraction 0< < 1 of infected people are too sick to work. This implies that during the pandemic the effective labour force E(t) is given by (1) (2) (3) E(t) = (1 - I (t))L, where we assume the labour (I) is fixed and does change over time. Finally, assume that production is Cobb-Douglas such that Y(t) = K (AE(t))¹-a, where capital is fixed (K) and technology (A) are fixed. (a) Find an expression for the growth rate of output in terms of the growth rate of infections 91 = 1/1(t). Is output growth positively or negatively related to infection growth? (b) Let K = A = L = 1, a = 0.33, p = 0.5, S(0) = 1, and the solution path for infections be I(t) = 1- S(t) + In(S(t)/S(0)). Create a MATLAB graph that plots output against the percentage of the population that is susceptible. Compare Ro = 2.5 to Ro = 1.4, where the latter is the average Ro of seasonal influenza. Assuming o is the same for Covid and influenza, is Covid's impact on the economy similar to influenza in this model? (Tip: set the axes to go no higher than 1, e.g. axis ([0 1 0.5 1]) so that only values of I(t) >0 are shown.) Ro Let's consider the economic impact of the pandemic on the economy. Assume that the pandemic evolves according to the basic SIR model: S i R and = = = -BS(t)I(t) BS(t)I(t)-I(t) yI (t) with initial conditions S(0), I(0), and R(0), satisfying S(0)+1(0) +R(0) = 1 S+I+R=0= S(t) + I(t) +R(t) = 1 for all t > 0. Assume that some fraction 0< < 1 of infected people are too sick to work. This implies that during the pandemic the effective labour force E(t) is given by (1) (2) (3) E(t) = (1 - I (t))L, where we assume the labour (I) is fixed and does change over time. Finally, assume that production is Cobb-Douglas such that Y(t) = K (AE(t))¹-a, where capital is fixed (K) and technology (A) are fixed. (a) Find an expression for the growth rate of output in terms of the growth rate of infections 91 = 1/1(t). Is output growth positively or negatively related to infection growth? (b) Let K = A = L = 1, a = 0.33, p = 0.5, S(0) = 1, and the solution path for infections be I(t) = 1- S(t) + In(S(t)/S(0)). Create a MATLAB graph that plots output against the percentage of the population that is susceptible. Compare Ro = 2.5 to Ro = 1.4, where the latter is the average Ro of seasonal influenza. Assuming o is the same for Covid and influenza, is Covid's impact on the economy similar to influenza in this model? (Tip: set the axes to go no higher than 1, e.g. axis ([0 1 0.5 1]) so that only values of I(t) >0 are shown.) Ro
Expert Answer:
Answer rating: 100% (QA)
To solve this problem we need to follow these steps a Find an expression for the growth rate of output in terms of the growth rate of infections From ... View the full answer
Related Book For
Microeconomics
ISBN: 9781464146978
1st Edition
Authors: Austan Goolsbee, Steven Levitt, Chad Syverson
Posted Date:
Students also viewed these accounting questions
-
An economist worrying about the economic impact of environmental regulations would model that impact with a a. Decrease in aggregate supply. b. Increase in aggregate supply. c. Decrease in aggregate...
-
Explain the economic impact of the US civil war in detail.
-
Define the economic impact of biofuel. What kinds are already used in the US? What is the future application in the US?
-
(a) Write the chemical reactions whose equilibrium constants are Kb and Ka for imidazole and imidazole hydrochloride, respectively.
-
Describe the seven tools of quality control. Are some more important than others? Would you use these tools separately or together? Give some examples of tools that could be used together.
-
AutoInnovate Inc., a company in the automotive industry, acquired a new robotic assembly line for its manufacturing plant in late 2 0 2 5 for a total cost of $ 1 2 0 million. Considering the relevant...
-
Analyze the housing price data in Table B. 4 for multicollinearity. Use the variance inflation factors and the condition number of \(\mathbf{X}^{\prime} \mathbf{X}\). y X1 X2 X3 X4 X5 X6 X7 Xg 25.9...
-
Suppose demand and supply are given by Qd = 60 - P and Qs = P - 20. a. What are the equilibrium quantity and price in this market? b. Determine the quantity demanded, the quantity supplied, and the...
-
What is the price of a 0.75 year European put option on a dividend-paying stock, where the stock price is $ 57, the strike price is $ 67, and a dividend of $ 0.61 is expected in 0.25 years?
-
Values for the NASDAQ composite index during the 1,500 days preceding March 10, 2006, can be downloaded from the authors web site. Calculate the one-day 99% VaR and the one-day 99% ES on March 10,...
-
A state has a 5/35 lottery game. The ticket costs 1$. Matchingall 5 numbers (jackpot) pays 200,000$, matching 4 of the 5 numberspays 200$ and match- ing 3 of the 5 numbers pays 2$. The rest ofthe t 1...
-
For each partition, propose a division of the profits that makes each firm at least as well off relative to independent action. Then show how one or more firms can actually do better in a coalition...
-
Consider the market for electricity. Suppose demand (in megawatt hours) is given by \(Q=50-P\) and that the marginal private cost of generating electricity is \(\$ 10\) per megawatt hour ( \(P\) is...
-
Consider a pollution problem involving a paper mill located on a river and a commercial salmon fishery operating on the same river. The fishery can operate at one of two locations: upstream (above...
-
When sulfur dioxide is emitted into the air it is transported over long distances and is converted to sulfuric acid. This gradually falls to the ground, either as rain or snow or simply by settling...
-
Suppose we have an agricultural valley \(100 \mathrm{~km}\) by \(50 \mathrm{~km}\), with a polluting electricity power plant. The power plant causes pollution problems in a narrow strip of land...
-
a)Delta of the share when price is between $50 and $51 = b)Delta of the share when price is between $51 and $52 = c)Gamma of the share when price is between $50 and $52 = Could you please provide...
-
Shreemaya Hotel in !adore was facing a problem of low demand for its rooms due to off season. The Managing Director (MD) of the hotel, Mrs. Sakina was very worried. She called upon the Marketing...
-
With the production function Q = 2 min(K, L) and the cost function C = 2K + 3L, what combination of inputs minimizes costs for Q = 10? Show this solution graphically.
-
Suppose that in a particular market, the inverse demanded for hasenpfeffer is given by P = 100 - Q. The market is served by two Cournot competitors, Hansel and Gretel, whose quantities are denoted qH...
-
Suppose that Maureen believes that name-brand laundry detergent is twice as effective as generic laundry detergent but that the two goods are otherwise identical. Therefore, her utility function is...
-
How and why would a country give up any of its sovereign powers?
-
As you have seen in this chapter, international trade law is founded on the importance and benefits of removing trade barriers. However, WTO rules also recognize the need to restrain trade in certain...
-
Could a contract be difficult to categorize as either public or private international law? What would such a contract look like?
Study smarter with the SolutionInn App