1. The expenditure relationship Y ≡ C + I + G + NX is an effective model to examine how GDP would fall with a decline in government expenditure G.

2. Consider the Lucas-style endogenous growth model presented in class and in the Williamson book. If u = , then the economy will be in the steady-state outcome with no growth.

3. The optimal behaviour for the government is to maximize the country’s GDP as this makes everyone as rich as possible (hint: a graph may prove helpful, but is not necessary to get full marks).

4. Consider a the one-shot version of the two-sided search model from lecture/the book with the matching function m(Q, A) = min{Q, A}. Furthermore assume the labour force is normalized to 1 (i.e. Q = 1). This economy would have no “frictions” where frictions are defined as a situation where vacant firms and unemployed workers co-exist1.

5. Suppose the economy is currently at the steady state in the bathtub model of unemployment. If both s and f permanently fall, then the new steady state will have a lower unemployment rate.

1. (Total: 20 points) Suppose you are given the following information about an economy. The economy exists for one period and there is no international trade. The overall economy can be modeled using a representative agent, a representative firm, and the government.

◦ Suppose the representative agent has preferences the can be model with the utility function: u(C, ℓ) = C −  (48 − 3ℓ)2

where C is the consumption and ℓ is the leisure. Suppose the representative agent sleeps 8 hours a night with the remaining 16 hours of their time split between leisure and labour Ns . The agent is paid a real wage of w, has a non-labour market income of γ, and pays a lump-sum tax of T.

◦ The representative firm in the market utilize the following production function: Y = 27(K)α (Nd)1−α

where K is fixed at 512 units, α = 1/3, and Nd is the firm’s labour demand. Workers are paid a real wage of w and capital is paid a real rental rate r.

◦ For part (a) assume government expenditure G = G¯ is 0. In parts (b) and (c), we will assume G¯ > 0

(a) (10 points) Suppose that both the goods and factor markets are perfectly competitive, what is the real wage w? (Hint: solve Ns = Nd .) After find the real wage rate, what is the real rental rate r in the economy?

Reminder: the expected profit of the representative firm in a 1-period model is simply normal long-run economic profits in a perfectly competitive equilibrium, i.e. zero economic profits.

(b) (5 points) Assume the capital is owned by the households meaning γ is the income from owning capital (i.e.  γ  = r × K¯ ).  Use this information to create a graph showing the consumption-leisure (or labour-leisure) outcome. Make sure to provide a numerical value for the optimal choice of leisure ℓ* and consumption c* . Assume G¯ = 100 and explain how different values of G would affect the graph?

(c) (5 points) Instead of a particular value, suppose G = G¯ > 0 here.  What is the social planner’s problem? Explain why the social planner’s problem will be Pareto Efficient (hint: a graph may prove helpful, but is not necessary to get full marks).