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(Solved) ASSIGNMENT 2, PROBLEM 2: INCOME AND SUBSTITUTION EFFECTS Suppose the consumer has 12 hours in a day, and the real wage is 1. The government enacts an...


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ASSIGNMENT 2, PROBLEM 2: INCOME AND SUBSTITUTION EFFECTS

Suppose the consumer has 12 hours in a day, and the real wage is 1. The government enacts an income tax, where they take a fraction .25 of the total wages earned by the consumer.

In your attached work, please be sure to write out the consumer’s optimization problem. Write out any decimals to 2 decimal places.

Part a: Write the consumer’s budget constraint with this income tax.

Part b: Does the income effect of this tax increase (↑), decrease (↓), not change (NC), or have an uncertain effect (?) on consumption, leisure, and labor supply? (Write it in short form, e.g.: C↑, l↓, Ns NC)

Part c: Does the substitution effect of this tax increase (↑), decrease (↓), not change (NC), or have an uncertain effect (?) on consumption, leisure, and labor supply? (Write it in short form, e.g.: C↑, l↓, Ns NC)

Suppose the consumer had preferences described by .

Part d: Write the consumer’s demand function for consumption as a function of the wage and the tax (leave the wage and tax as variables).

Part e: Write the consumer’s demand function for leisure as a function of the wage and the tax (leave the wage and tax as variables). Based on this demand function, does the consumer’s optimal quantity of leisure increase, decrease, not change, or have an uncertain effect when the wage increases?

Part f: Graph the consumer’s budget constraint without the tax and the consumer’s budget constraint with the tax. Label which budget constraint is which, the intercepts of the budget constraints, and any corners on the budget constraints. (Please graph this on the 3rd page of the solutions sheet.)

Part g: Suppose the consumer had a utility function such that for leisure, the substitution effect of an income tax increase was larger than the income effect (this may be different from the consumer’s utility function given above). On the graph you made for Part f, graph two indifference curves so the optimal bundles with the tax and without the tax show this relationship.


ASSIGNMENT 2, PROBLEM 3: FIRM OPTIMIZATIONSuppose the firm has the production function(function in the file attached). It owns 27 units of capital and its total factor productivity is 1. Assume there is no cost to owning or renting capital.Please show your steps in your attached work. Write out any decimals to 2 decimal places.Part a: Write the firm’s profit function.Part b: Write the firm’s demand for labor demand as a function of the wage.






 


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