代做Econ 323 Comprehensive Problem Set B3代做留学生Matlab编程

Econ 323

Comprehensive Problem Set (CPS) Block 3.

This problem set will be made up of three blocks.  Block 1 and 2 are published previously.  This block corresponds to material between MT2 and MT3.

The CPS is optional.  All three blocks are required to complete the CPS.

If a student elects to do it, the CPS score may replace one of the three midterm exams. The CPS can replace a low midterm score, or if a student has not taken one of the exams for some reason, it can fill in for the missing test.  It is fine if a student wishes to opt-out of MT3 and use the CPS to fill in the gap.

As described in the syllabus and in class, the CPS is intended to be incrementally more challenging than the “standard” practice problems or exam problems we do routinely.  You can think of it as a “stretch” assignment. All questions will have a small novelty or two that the student needs to work out on their own. The problems should then seem harder than our “standard” work.

The use of AI to answer these questions is against the spirit of this optional assignment. Please refrain from using AI to answer these questions.  Using Desmos is fine and encouraged, but not required.  While this is not a group assignment, talking to other students is also fine, IF 1) those conversations are geared to all students trying to understand and complete the problems and 2) each student is doing the bulk of the work themselves, as opposed to one student solving the problems and letting others put their names on their submissions.

Answer each of the following two questions.

1. (50 points)We will imagine there being two markets for computers:  Home computers and Business computers. The curves in these markets are linear, but I will not tell you what those formulas are [you don’t need to know them to answer the questions].  However, I will tell you that at the equilibrium, the elasticity of demand for home computers is -2.5, the elasticity of demand for business computers is -.90, and the elasticity of supply for computers for both purposes is 1.

a. (10) A per-unit tax of $200 is imposed on the suppliers of computers.  How much does the buyer price increase in each market?  You can and should do this without knowing anything about the pre-tax equilibrium, if you use the elasticity formulas we covered in lecture.

b. (10) Suppose the untaxed market equilibrium price and quantity in the home computer market are $850 and 10.5 million, respectively.  In the business market, the untaxed market equilibrium price and quantity are $1200 and 15 million, respectively. What is the total revenue from the tax?

c. (10) What is the deadweight loss of the $200 tax?

d. (10) Comment on the relative sizes of the DWL in the two markets.  Why are they different?

e. (10) Suppose the government wishes to raise the same revenue as you found in part b, but to achieve this with a lower total DWL.  The government can do this if it can impose different per unit taxes for the Home and Business computer markets.  Qualitatively, compared to the original tax level of $200, how should the relative taxes on each computer type change?  I don’t want you to solve this numerically, but explain your reasoning.

2. (50 points)

A worker has 100 hours per week to allocate between labor L and leisure ℓ.

ℓ = 100 -L

The gross wage is w = 25. Wages are taxed at a proportional rate t, so the net-of-tax wage is:

w_t=w(1-t)

Consumption equals labor income:

C=w_t*L

The marginal utilities of consumption and leisure are given as:

MU_c=1,

MU_ℓ=(3.8597*10^-7)* ℓ⁵

a) (15 points) Using the marginal utilities. the wage information, and an initial tax rate of t0 = 0.20, determine the worker’s initial labor supply L0.

b) (15) Now suppose the tax increases to T = 0.25. Using the same marginal utilities, compute the new labor supply L1.

c) (10) Compute the percentage change in labor supply.

d) (10) What is the elasticity of labor supply?