Solve it plzzz

Gnnsider a one-period closed economy, i.e. agents (consumers, rms and government} live for one period, consumers supply labor and demand consumption good, whereas their utility limction is in N111! 1+1: and their production function is y = 2N1 "1. The government nances an exogenous spending via the form of log[c x :I [GI-[H preference]. Firms supply consumption good and demand labor lumpsum taxes. Suppose there is a positive shock on x which means the consumers favor leisure [or dislike labor] by much more than consuruption now, i.e marginal rate of substitution of leisure for consumption increases [indifference curves become steeper}. l. Analyze the effects of this preference shock on the consunlptionfleisure choice of the individual consumer given a constant wage and tax. Support your answer with appropriate graphs. 2. How is this change in consumer's preference transmitted to rm's problem? 1What will be the effect of this change on equilibrium quantities and prices (outputs, consumption, hours worked, and real wage]. Draw a labor demand and supply graph to analyze. 3. Now, suppose there is a social pla1mer who maximises consumer's utility subject to the re striction of resource constraint. Solve this social planner's problem and derive all analytic solutions (consumption, output, labor hours, and real wage]. How do the equilibrium quan tities and prices respond to the increase in x? Is that consistent with your intuition above? 4. Based on your answers above and our observations about business cycle in class, do you think that such a change in preferences might explain business cycles? Explain why or why not, with reference to the key business cycle facts. (Hint: 1You should cite some regularity of business cycle to answer this question, such as the cyclicality of consumption, working hours and wage rates.)