First Fundamental Theorem of Welfare Economics Essay

First Fundamental Theorem of Welfare Economics - Essay Example The third condition for competitive equilibrium is that the allocation maximizes the profit of each firm at the given price system. A simple proof of the theorem is shown in the following notation. Proof of the first fundamental theorem of welfare economics Let [(x0i), (y0j), (Ð ¤)] be a competitive equilibrium, and under the condition of non-satiation, for each: i, ui(x) = ui (x0i)†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ eqn. 1 implies Ð ¤ (x) ? Ð ¤ (x0i). Instead, if we denote this as: ui(x) = ui (x0i), and Ð ¤ (x) ui(x)= ui (x0i), 1, 2, †¦Ã¢â‚¬ ¦ Since Ð ¤ is continuous, this condition implies that, for a big n, Ð ¤ (xn) ui (x0i), implies that Ð ¤ (xn)>Ð ¤ (x0i). Therefore, the contradiction implies that eqn. 1 is true. Using this contradiction, we can suppose that the initial allocation [(x0i), (y0j), (Ð ¤)] is not Pareto optimal, which implies that there is another allocation of resources [(x’i), (y’j)] such that ui(x’i) > ui (x0i). this condition holds for all i with strict inequality for some i. Employing the second condition in the definition of competitive equilibrium, gives that for some instances of i, ui(x’i) > ui (x0i) gives the implication that Ð ¤ (x’i)> Ð ¤ (x0i). From eqn. 1 and the linearity of Ð ¤, it can be seen that k?i, where ui(x’k) > uk (x0k), ?k Ð ¤(x’k) k Ð ¤(x0i). For l?k, where ul(x’l)> ul(x0l), ?l Ð ¤(x)> ?l Ð ¤(x0i). Finding the sum of the equations across all i; , which contradicts the third condition of competitive equilibrium. 2. The theorem proved above is mathematically true; however, some drawbacks are associated with it, for example, when public goods and externalities are introduced. This is because the theorem assumes that in the economy, there are no public goods or externalities (Jehle and Reny, 2001). This means that the theorem will not hold in an exchange economy where an individual’s utility depends on another individual’s consumption as well a s the original individual’s consumption. Also, the theorem does not hold if the production possibility set of one firm in an exchange economy depends on the production set of another firm in the same economy. The presence of externalities and public good sin the market will cause market failure iof they are not corrected, since there are no markets for these goods. 3. The above proposition can be proved by the following example, where externalities and public goods are introduced into an economy. In this case, an externality is used to mean the situation where the actions of an individual or firm affects the actions of another individual or firm other than through the effect on prices (Jehle and Reny, 2001). For example, one production firm could be increasing the costs of production for another firm by the production of smoke, which forces the other firm to increase costs. One factory could be producing electronic gadgets, a process which requires the emission of smoke. The factory could be located upwind, meaning that the smoke emitted harm another

The Lebanon Crises (1958) Term Paper Example | Topics and Well Written Essays - 2500 words

The Lebanon Crises (1958) - Term Paper Example In Lebanon, the big problem was the fragile nature of the social and political structure of the country. Lebanon was a multi-confessional state with Christians and Muslims sharing power. The new Government appointed by President Chamoun in 1956 seemed to tilt more towards the West. On January 5, 1957, President Eisenhower appeared before Congress to announce a new US policy for the Middle East. He asked Congress to pass a resolution authorizing economic assistance and the use of US forces to prevent a Communist takeover in the Middle East (Meo 132-144). Lebanon was the only Arab country to announce publicly its support for the doctrine. The decision by President Chamoun to endorse the new US policy, and accept aid under the terms of the Middle East Resolution, caused a major foreign policy rift between the Government and the opposition in Lebanon and led to the formation of the united National Front, an opposition grouping composed of Muslims and Christians (Meo 132-144) This rift coincided with Chamoun's plans to amend the electoral law before the elections in June 1957. The passage of the new law increased the number of seats in the Chamber of Deputies and had a direct impact on the outcome of the elections, outside influences also affected the outcome. The United States provided covert funds for pro-Government candidates, while Egypt and Syria supported and funded the opposition (Eveland 248-250). Since assuming the Presidency, Camille Chamoun had made a determined effort to destroy the power of the feudal landowners who formed the backbone of the Lebanese political system.