Question

. Luxembourgers consume only coffee and cigarettes. Each Luxembourger has the same utility function u(x,y)-xay1-a, where x and y are the amounts of coffee and cigarettes consumed, and a є (0,1). Luxembourger i has income mi , and the aggregate national income is M - L.mi. The government wants to reduce the cigarette consumption byd percents using a tax. Suppose that after the introduction of the tax the price of cigarettes is simply (1 + t)py, where t is a tax rate. (a) (3 points) Find tax rate t that implements the d percents reduction in the nationwide cigarettes consumption. That is if x is the initial amount of cigarettes consumed, then after the introduction of the tax the new cigarette consumption is (1- d)x (b) (3 points) The introduction of the tax appears to be very unpopular among Lux embourgers. The government is afraid of loosing the support of voters, and decides to compensate them by distributing subsidies, such that the income with subsidy i:s m,(1 + s.). Find the subsidy si for each Luxembourger i, such that after the intro- duction of both, the tax from (a) and the subsidy, the utility of each i is the same as before the changes. Show that, to the annoyance of the government, after imposing the tax computed in (a) and compensating the people using subsidies Sí, does not achieve the goal of d percents reduction in smoking (c) Find a tax rate and a subsidy such that the government achieves d percents reduction in the cigarette consumption and the consumers receive the same utility as before the ах (d) (Hard) Show that the policy you computed in (c) is costly. That is show that total proceeds from cigarette taxation are smaller than the total subsidies payed out.

Answer 1

When we have two alternatives to any action, i.e. there are two ways to arrive at a certain conclusion , or there are two choices to physically or ethically consume a product, that choice between the two options is referred to as the binary choice model.

                                     There are various factors among the two binary choices that needs to be estimated to arrive at a conclusion or to finally choose any of the two choices, however, the most critical and the overall estimation that needs to be done is the ‘maximum likelihood’ of one of the options to be better than the other. We need to estimate which of the two choices has the maximum likelihood to achieve what we desire out of the two choices.

                                  The linear choice model studies the relationship of quality between the outputs of the choices we have. The output with the best qualitative relationship is better preferred in the linear model of choices. The model in which only two options are possible for an outcome is referred to as the probit model of choice. For example, if we want to know the gender of an individual, there will be only two options, Male or Female.

                                Choices are very intrigue between various individuals. Economics shows the various ways in which we can make the appropriate choice between two different, mutually exclusive or coherent choices.