CAS EC 571 Environmental Economics Fall 2022
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CAS EC 571 Environmental Economics
Fall 2022
Homework Assignment #1
Q.1. (30 Points) By searching various sources (international organizations websites, government institutions websites and white papers), find a real life projects that has one of each three objectives in environmental economics. For each project provide the full project title, funding/conducting agency, and description of the project in a small paragraph.
1. Objective I: Environmental Quality –
Project Title:
Financing and Conducting Agency/Institution:
About the Project:
2. Objective II: Sustainable Development –
Project Title:
Financing and Conducting Agency/Institution:
About the Project:
3. Objective III: Biodiversity –
Project Title:
Financing and Conducting Agency/Institution:
About the Project:
Q.2. (20 Points) In a 2x2 exchange economy, Z and K consume two goods, X1 and X2 . The utilities that both Z and K get from the consumption of these goods are given by the functions;
UZ (X1(Z), X2(Z)) = (X1(Z))1/4 . (X2(Z))3/4 and UK (X1(K) , X2(K)) = (X1(K))1/4 . (X2(K))3/4 , respectively. Before the exchange starts between the consumers, Z has 27 units of X1 and 18 units of X2 , that is (仙 1(Z), 仙 2(Z)) = (27, 18). K has 54 units of X1 and 9 units of X2 , that is (仙 1(K), 仙 2(K)) = (54, 9).
a. Draw Edgeworth Box of this economy. Clearly mark the axes, size of the box and mark the endowment point.
b. What is the relative prices that will set the market to the equilibrium?
Q.3. (50 Points) Consider an economy with two individuals (1 and 2), a dirty good (X), a clean good (T), and labor as the only input to the production. The utility of each individual is defined as Ui (Xi , Ti , E) for i = 1, 2 where Xi and Ti are the consumption levels of the two goods and E is an exogenous (to the individual) level of pollution emissions. Production of X releases the emissions, E . The production of X can be defined as X = f(LX , E), where both labor input LX and emissions E have a positive marginal products. This specification treats emissions as an input, as the reduction of pollution reduces the output of X by decreasing the productive factor. The clean good T is only produced by labor input following the production function T = g(LT ). Labor employed in the economy is constrained by the work time endowment such that LX + LT = .
Answer the following question in (A) (i)-(iv), (B) (i)-(vi), and (C).
(A) Given the following analytical presentation of the Pareto Efficiency problem of the economy, answer the questions in (i)-(iv).
Pareto Efficiency:
max U1 (X1 , T1 , E) + 入U . [U2 (X2 , T2 , E) − ̅] + 入X . [f(LX , E) − X1 − X2 ]
X1 , X2,T1 , T2, LX, LT,E
+ 入T . [g(LT ) − T1 − T2 ] − 入L . [ − LX − LT ]
where individual 1’s utility is being maximized subject to the constraint that individual 2 obtains at least utility level of 2, and where 入U, 入X, 入T and 入L are the Lagrangian multipliers of the constraints.
(i) Write down the first order conditions of Pareto Efficiency problem. (ii) Write down the expression (equation) for “efficiency in consumption.” (iii) Write down the expression (equation) for “efficiency in production.” (iv) Write down the expression (equation) for “efficiency in product mix .”
(B) Suppose Px and PT denote the prices of X and T, respectively. Furthermore, let the price of labor be w and the income of person i is Yi .
(i) For individual i, write down the utility maximization problem and the first order conditions.
(ii) Write down the expression (equation) for “efficiency in consumption.” (iii) Write down the profit maximization problem of firm T and its first order
condition.
(iv) Write down the profit maximization problem of firm X and its first order
conditions.
(v) Write down the expression (equation) for “efficiency in production.” (vi) Write down the expression (equation) for “efficiency in product mix.”
(C) Rewrite the first order conditions for emission (from part (A) and (B)) and then make a comparison of the efficient allocation of emissions in (A) and (B).
2022-10-02