Business, 20.09.2020 17:01 341404143

Suppose the representative agent has a utility function over consumption, c, and leisure, l, which takes the form: u(c, l) = ln(c) + 2Dl D is a constant greater than 1.

Suppose the consumer faces a tax rate, t, on her labor income (i. e. she pays t dollars on every dollar earned). Further, assume that we are in a one-period setting (so there is no borrowing) and the agent takes the real wage, w, as given.

a. Do these preferences admit diminishing marginal utility in consumption? On leisure?
b. Write the budget constraint.
c. Using the Lagrangian method, solve for the labor supply function. Putting price (w) on the y-axis, and quantity (optimal n) on the x-axis, graph it.
d. What happens to the labor supply in response to a tax rate increase? What is the intuition for this result (remember prices and preferences determine allocations)?
e. How does labor supply respond to an increase in D? Provide intuition.

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Suppose the representative agent has a utility function over consumption, c, and leisure, l, which t...

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