(a) Derive the uncompensated (Marshallian) demand functions. (7%)

(b) Derive the compensated (Hicksian) demand functions. (7%)

(c) Explain the differences between the uncompensated demand and the compensated demand. (6%)

(a) What is the shutdown price for an individual firm in the short run? (5%)

(b) Derive the short-run market supply function. (5%)

(c) Find the equilibrium price and quantity in this market. (5%)

(a) Suppose the firm can distinguish between the two groups of consumers and is able to engage in third-degree price discrimination. Determine the profit-maximizing price and quantity for each group. (10%)

(b) Based on your answer in part (a), explain why the monopolist charges a higher price in one group than in the other. (5%)

Part II 1. Consider a Mundell-Fleming model (IS-LM-BP) for a small open economy with perfect capital mobility. The model is described by the following equations: Goods market: $$Y = C(Y) + I(r) + G + NX(e)$$ Money market: $$\frac{M}{P} = L(r, Y)$$ Foreign exchange market: $$r = r^*$$ where Y denotes output, C is consumption, I is investment, G is government spending, NX denotes net exports, r is the domestic interest rate, e is the exchange rate (defined as the amount of foreign currency per unit of domestic currency), and r* is the given world interest rate. Using this model, analyze the impact of an expansionary fiscal policy (an increase in government spending) on output and its effectiveness under (a) a floating exchange rate regime and (b) a fixed exchange rate regime.     Illustrate your analysis using IS-LM-BP diagrams     and provide a detailed explanation of how the economy adjusts to a new equilibrium. (10%)

(a) Derive the steady-state level of capital per worker \( k \) and the steady-state output per worker \( y \), where \( k = K / L \) and \( y = Y / L \). (5%)

(b) Compute the long-run growth rate of output per worker \( y \) and total output \( Y \), and explain why the Solow model is considered an exogenous growth model. (5%)

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