1) Consider a small community of 100 identical individuals who consume a private consumption good x and a public good z. Each individual's preferences are defined over the two goods as follow: Ui = 5xi + 2z^(1/2). The cost of producing z is Cz(z) = 200 +4z, the cost of producing x is Cx(x) = 100+x.
a) What would be the efficient provision of the public good in this community?
b) Find the market allocation guided by competitive equilibrium prices and identify the inefficiency of the "invisible hand."
2) Identify True or False and explain the economic logic under each statement.
a) The classical dichotomy implies that aggregate demand depends on neither the money supply nor the general price level.
b) The classical model implies that the sharp decline we have observed in the price of oil over the past six months is irrelevant for the determination of equilibrium output and input.
3) The closed-economy version of the Classical model: Y = F(K, L) C = C + a(Y - T), with C, a >0, I = I - βr, with I, β > 0, where C and I represent the exogenous components of consumption (C) and investment (I) respectively. Assume the factor inputs are fixed in supply, K = K , L = L, and that fiscal policy is also fixed: T = T and G = G
a) Predict the effects of an exogenous increase in consumption C on equilibrium output (Y), investment (I), and the interest rate (r).
b) How and why would your predictions change if consumption (C) also depends negatively on the interest rate (r)?