Solve it plzzzz

Consider a one-period closed economy, i.e. agents (consumers, firms and government) live for one period, consumers supply labor and demand consumption good, whereas their utility function is in the form of log(c - X It) (WIT ) (GHH preference). Firms supply consumption good and demand labor and their production function is y = =NV]-". The government finances an exogenous spending via lump-sum taxes. Suppose there is a positive shock on x which means the consumers favor leisure (or dislike labor) by much more than consumption now, i.e marginal rate of substitution of leisure for consumption increases (indifference curves become steeper). 1. Analyze the effects of this preference shock on the consumption/leisure 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 firm's problem? What 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 planner who maximizes 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: You should cite some regularity of business cycle to answer this question, such as the cyclicality of consumption, working hours and wage rates.)