Question

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−χN1+ν/1+ν ) (GHH preference). Firms supply consumption good and demand labor and their production function is y = zN^1−α. The government finances an exogenous spending via lump-sum taxes. Suppose there is a positive shock on χ 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. (Hint: Solve for C∗ and N∗ as a function of exogenous parameters. You’ll notice that change in χ leads to a pure substitution effect by making the indifference curve steeper. This is like rotating the indifference curve towards higher leisure since you have a higher preference for leisure now. This parameter does not appear in the budget constraint and therefore will not lead to any income effect. In earlier homework, all the changes came from the change in the budget constraint by either shifting your budget constraint (change in T that led to pure income effect) or changing the price of leisure w (that led to income and substitution effect). Now there is no change in income but change in preference that shows up by changing the shape of indifference curve by keeping budget constraint same.)

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 (hours worked N, and real wage w). Answer this question using labor demand and supply graph. (Hint: You’ll notice that there is a change in consumer labor supply as a result of change in χ whereas firm’s labor demand is fixed. Think about how will firm respond to either an increase or decrease in the labor supply.)

3. Now, suppose there is a social planner who maximizes consumer’s utility subject to the restriction 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 quantities and prices respond to the increase in χ? Is that consistent with your intuition above? (Solve for SPP by maximizing consumer’s utility with respect to resource constraint. Solve for N∗, Y∗, C∗, w∗ by equating w∗ = MPN (remember that CE is same as SPP under “certain conditions” and so you can still find the solution of w∗ from the SPP) and see what happens when there is change in χ. You should have same response of all endogenous variables to change in χ as in part (a).)

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. Some examples are in the textbook as well.)

Answer 1