Intermediate macroeconomic II.please help solve

3. Suppose that the representative consumer's preferences change, in that his or her marginal rate of substitution of leisure for consumption increases for any quantities of consumption and leisure. (a) What effects does this have on the equilibrium real wage, hours worked, output, and consumption? (b) Do you think that preference shifts like this might explain why economies experience recessions (periods when output is low)? 4. Country A is located on a small island that is isolated from the outside world. The country has one representative consumer, whose preference is represented by: U(c, l) In(c) + In() There is one representative firm in the economy which is owned by the consumer, it produces one type of good that can be used for consumption or government expenditure using capital and labour as inputs. The firm owns the capital it uses and it's production technology is represented by F(K, N) KN-a where z is the total factor productivity, and a is the capital share of income. The firm pays all of its profit back to consumer as dividend. The government of country A spend a pre-determined G amount of goods to provide public 1 services, and it taxes consumer through a lump-sum tax t to finance the expenditure. the government's budget is balanced: G=t Now, suppose that the firm cannot change its capital stock, or improve its production tech- nology in the short period, such that z and K are given. (a) When describing this economy as an macroeconomic model, what is the set of exogenous variables? What is the set of endogenous variables that can be determined given the set of exogenous variables using the concept of Competitive Equilibrium? (b) Define the competitive equilibrium for this economy, be specific about what it is, what conditions have to be satisfied, who solves what problem and etc. (c) List the set of equations that will be used to determine all of the endogenous variables. Which four of these endogenous variables are essentials, such that once you know these four, all other endogenous variables can be obtained easily? (d) Write down the four equations that can be used to solve for these four essential endoge- nous variables, and describe where do they come from. Describe in details the steps of how would you solve for the competitive equilibrium (without actually solving for it). (e) Setup the Social planner's problem for this economy. What is the marginal condition that pins down the planner's choices. (f) Now, describe what would happen to c", 1", and w" if the firm had more capital, such that Knew > Kold. 5. In the simplified model with proportional taxation, there can be two equilibria, one with a high tax rate and one with a low tax rate. Now, suppose that government spending increases. Determine the effects of an increase in G on consumption, leisure, labour supply, real output, and the tax rate in a high-tax equilibrium and in a low-tax equilibrium. How do your results differ? Explain why.