Write down an exchange economy model with two individuals and two goods, in which there is no consumption externality. State and explain the key assumptions of the model. Using the model, answer the following questions: (a) Explain carefully how the concept of Pareto efficiency differs from that of social welfare. (b) State the Second Theorem of Welfare Economics and explain carefully why it holds. What is the importance of the assumption of convex preferences to this theorem?

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Assume you have a two-good model:  Beverages are on the X axis and Food on the Y axis. You have a $400 budget. The price of beverage is $10, and the price of food is $20. a. Graphically illustrate the budget line correctly. b. Now assume the price of food decreases to $10 ceteris paribus. Graphically note the change on the same graph. PLEASE SOLVE THIS QUESTION WITH PROPER AND UNDERSTANDABLE GRAPH

2. The standard model of consumer behavior assumes that income is exogenous. Of course, a person's income usually depends upon the number of hours the individual works. Suppose that an individual has T hours each day which can be allocated toward working time, H, or leisure time, L-that is, T = H + L. The individual earns w dollars for each hour worked. Then the individual's income is M + wH where M denotes any non-labor income. The individual has preferences over leisure time, L, and a consumption good, X, which can be represented by a quasi-concave utility function, U(X, L). The consumption good, X, can be purchased at the price Px. The individual seeks to maximize the utility subject to the constraints on time and money. (1) Formulate the individual's problem as an optimization problem with two constraints a time constraint and a money constraint. Derive the first-order conditions. Give an economic interpretation of the Lagrange multipliers. (2) The two-constraints problem can be…