Consider a duopoly market, where two firms sell differentiated prod- ucts, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices pi and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = } + and D2 (P1, P2) = {+ , where S > 0 and the parameter t >0 measures the degree of product differentiation. Both firms have constant marginal cost c > 0 for production. 2t (a) Derive the Nash equilibrium of this game, including the prices, outputs and profits of the two firms. (b) From the demand functions, q; = D; (pi, p;) = § + , derive the residual inverse demand functions: p; = P;(qi, P;) (work out P;(qi, P;)). Show that for t > 0, P;(qi, P3) is downward-sloping, OP (41-P;) < 0. Argue that, taking p; 2 0 as given, firm i i.e., is like a monopolist facing a residual inverse demand, and the optimal q: (which equates marginal revenue and marginal cost) or p; makes P:(q;, P;) = På > c, i.e., firm i has market power. (c) Calculate the limits of the equilibrium prices and profits as t → 0. What is P:(qi, P;) as t → 0? Is it downward sloping? Ar- gue that the Bertrand Paradox (i.e., the prediction of the static Bertrand duopoly model, where p¡ = p = c) holds only in the extreme case of t = 0.

Federal law allows workers who leave a job to continue to participate in the health insurance they were receiving through their previous employer. However, they have to pay the full monthly premium (including both the employee and employer portions), as well as a 2 percent administrative fee. This high price has led many people, especially the healthier ones, to drop coverage. Insurance companies report that these plans lose them money.  This phenomenon is an example of: a. Adverse Selection b. Moral Hazard c. Tragedy of the Commons d. Commodity Egalitarianism

B.You are interested in the relationship between health and income at individual level. If you had no practical, financial, or ethical constraints, how would you determine if education had a causal impact on health at? Question 2: a. Provide definitions of “sustainable development”: first, according to the Brundtland Commission (1987) and second, according to how most economists would define it.

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interest). At what age is the rate of disease development the highest? Source: Adapted from P. Coleman et al., “Endemic Stability―A Veterinary Idea Applied to Public Health," The Lancet 357 (2001): 1284–86. 19. If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. The marginal cost is the rate of change of the cost with respect to the number of items produced, that is, the derivative C'(x). (a) Show that if the average cost is a minimum, then the marginal cost equals the average cost. (b) If C(x) = 16,000 + 200x + 4x³/2, in dollars, find (i) the cost, average cost, and marginal cost at a produc- tion level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost. 20. If R(x) is the revenue that a company receives when it sells x units of a product, then the marginal revenue function is the derivative R'(x). The profit function is

How did you get step 2? I am confused on how you went from  dQ/dE= 6*1/2*E-1/2 to VMP=6*6*1/2*E-1/2

Explain a main point in Maki Naro's "Vaccines Work. Here Are the Facts" for rhetorical analysis essay