3. Monetary Neutrality

III. Short Answer Questions (簡答題)(50%) 1. (15%)Suppose that the inverse market demand curve for cloth is $P = 150 2Q$, the private marginal cost (unregulated competitive market supply) is $MC^p = 75 + Q$, and the marginal damage from pollution is $MC^d = 2Q$. a. What is the unregulated competitive equilibrium quantity and price?

b. What is the social optimal quantity and price?

c. What specific tax rate \( t \) (per unit) would result in the social optimum?

2. (10%)Consider the Solow growth model without technological change. The production function is $Y = K^{1/3}L^{2/3}$, where $K$ and $L$ represent the total capital and workers used, respectively. The parameters of the model are given by $s = 0.36$ (savings rate) and $d = 0.04$ (depreciation rate). Let $k$ denote capital per worker; $y$ output per worker; $c$ consumption per worker; $i$ investment per worker. Find the steadystate level of the capitallabor ratio, $k^*$, if the population grows at fixed rate $n = 5\%$.

3. (10%)Use the classical ADAS model to analyze the following statement, and show what would happen in the long run if such advice were followed by the Central Bank: The increase in the stock market has increased people's wealth. As a result, their consumption has increased, increasing aggregate demand and output. Hence the Central Bank needs to increase the money supply, since with higher income, people's demand for real money balances will be higher.

4. (15%)Suppose the utility function for goods $x$ and $y$ is given by $$U(x, y) = xy + y.$$ a. Let \( P_{x} \) and \( P_{y} \) be the price of \( x \) and \( y \). Calculate the expenditure function for \( x \) and \( y \). b. Compute the compensated demand functions for goods \(x\) and \(y\).

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