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Question

Country A is located on a small island that is isolated from the outside world. The countryhas one representative consumer, whose preference is represented by:U(c, l) = ln(c) + ln(l)There is one representative fi rm in the economy which is owned by the consumer, it producesone type of good that can be used for consumption or government expenditure using capitaland labour as inputs. The fi rm owns the capital it uses and it's production technology isrepresented byF(K;N) = zK^aN^1-awhere z is the total factor productivity, and a is the capital share of income. The fi rm paysall of its profit back to consumer as dividend.The government of country A spend a predetermined G amount of goods to provide publicservices, and it taxes consumer through a lump-sum tax t to finance the expenditure. thegovernment's budget is balanced:G = tNow, suppose that the firm cannot change its capital stock, or improve its production technology 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 exogenousvariables? What is the set of endogenous variables that can be determined given the setof exogenous variables using the concept of Competitive Equilibrium?(b) Defi ne the competitive equilibrium for this economy, be specific about what it is, whatconditions 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 thesefour, all other endogenous variables can be obtained easily?(d) Write down the four equations that can be used to solve for these four essential endogenous variables, and describe where do they come from. Describe in details the steps ofhow 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 conditionthat pins down the planner's choices.(f) Now, describe what would happen to c, l, and w if the firm had more capital, suchthat Knew > Kold.