14. For the following differential equation 1 = 2vc - 0.251, = > 0 (a) Find all steady-state(s) (equilibria, fixed points). (b) Using linear approximation describe local asymptotic stability of the steady-state(s).12. For the following differential equation 1=rto-4(2+1) (a) Find all steady-state(s) (equilibria, fixed points). (b) Using linear approximation describe local asymptotic stability of the steady-state(s).13. In a macroeconomic model C(t), /(t), and Y(#) denote respectively the consumption, invest- ment, and national product in a country at time t. Assume that, for all f : Y(t) = C(t) + I(t) I(t) = 20(t) C(t) = =Y(0) +b where b is a positive constant. (a) Derive the following differential equation for Y (t) : Y(t) = }Y(t) -b. (b) Solve this equation when Y(0) = Yo, >0 and then find the corresponding I (t).(a) (4 points ) A uniform pricing monopolist has an upward sloping MC curve. Claim: a price ceiling set below the monopoly price will increase welfare relative to the monopoly outcome ( assume the monopolist does not shut down).[h] [4 points] A large box of paper towels which will last you 2 years is on deep discount at \".l'vai'al-I'IlartI saving you $1 per roll. Claim: a rational consumer who has perfectly.r inelastic demand for paper towels should always purchase this large ho}: instead of paying a higher price for individual paper towel rolls. (c) (4 points ) In an oligopolistic market with identical firms, the market price is higher when there are two firms in the market than when there are 100 firms in the market.(d) (4 points) The government of a developing country is worried about the adverse effect that the high interest rate in the economy has on investment. Claim: Since a low interest rate makes more projects have positive NPV, investment in this economy will increase if the government imposes an interest rate cap.[e] [8 points] There are three individuals in society: Boh, Milton and Paul. There are three possible social st ates which result in different utility levels for the three individ- uals: --- Are the following True fFalserncertainT Explain. [i] No government would choose social state E. [ii] There is a government election in this society and there are two candidates: a Rawlsian and an Utilitarian government candidates. Claim: In a democratic election {majority win election] a Utilitarian candidate will he elected since more individuals in this society prefer the Utilitarian candidate. [g] [4 points] Marco's monthly income is $10M. He spends 4% of his income on food and the rest on buying designer clothes. The City Council thinks it is unfair that people spend more than 35% of their income fer food. In order to lower the proportion of income going to foodI the City Council gives Marco HUI]. Claim: given that Marco's income elasticity of food is 2. the City Council accomplishes its goal