Spring 2018 Intermediate Microeconomics (ECON 3110) Assignment help

DEPARTMENT OF ECONOMICS & FINANCE
College of Business, Tennessee State University, Nashville, TN, USA
Spring 2018 Intermediate Microeconomics (ECON 3110)
COMPREHENSIVE FINAL EXAMINATION

ANSWER ALL QUESTIONS IN ASMUCH DETAIL AS POSSIBLE. SHOW
YOUR DETAILED WORK.
1. Consider a world with no income and sales taxes. The utility function of a represen-
tative consumer is given by u = px1x2.
Her budget constraint is given by 7×1 + 10×2 = 3000.
Solve for the optimal consumption bundle that the consumer will choose.
Now suppose the government is debating between a 9:75% at sales tax on both the
commodities or a 5% income tax.
The government is going to have either the sales tax or the income tax but NOT both.
Solve for the optimal consumption bundles under sales tax and under income tax
regimes separately.
Which regime (sales tax or income tax) raises higher revenue for the government?
Calculate the precise revenue collection in each scenario.
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Which regime (sales tax or income tax) results in higher consumption for our repre-
sentative consumer?
Which regime (sales tax or income tax) results in higher utility for our representative
consumer?
If there are one million consumers like our representative consumer, how much of the
two commodities will be demanded in the economy? (Compute the total demand with
NO taxes and then with sales and income taxes. Now compares these three sets
of numbers and reect on their di¤erences.)
2. Consider three consumption bundles X; Y;Z.
Prove that if X is preferred to Y and Y is preferred to Z then X is preferred to Z:
Use the insight from this proof to show that two indi¤erence curves may not intersect
one another.
3. Suppose two commodities are perfect complements and the consumers utility function
is given by U = minfX1;X2g.
Both the commodities are priced the same way and they cost $20 per unit. The
consumer makes $2000.
Write down the budget constraint of the consumer.
How much amount for each of the commodities will the consumer consume and why?
What will be the utility level of the of the consumer if she is maximizing her utility
subject to the budget constraint?
4. Argue in EACH case below as what returns to scale the production function exhibits
(Show reason behind your conclusion):
f(x1; x2) = x1 + x2;
f(x1; x2) = (x1 + x2)2;
f(x1; x2) = (x1 + x2)1=2
5. Critically assess if the following statements are true or false:
(You MUST provide 3 4 linesof explanations for EACH answer and draw graphs
wherever you can. Providing crisp mathematical explanation wherever possible will be
good.)
i) MC intersects the AV C where AV C is minimum.
ii) MC intersects the ATC where AV C is minimum.
iii) Break-even point refers to the point where MR = MC
6. The inverse demand curve faced by a monopolist is given by P = 200010Q. Monop-
olists marginal cost is constant is given by c = 25.
Assume that the monopolist maximizes its prots.
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What is the amount that the monopolist would produce and what will be the market
price?
Compute the total prot of the monopolist and also the value of the consumer surplus.
7. Consider Question #6 and assume that the market is served by two rms playing a
Cournot game. Their constant marginals costs of production are given by c1 = 20 and
c2 = 25. Assume that both rms are prot maximizers.
Compute the output produced by each of the rms. Also compute the aggregate supply
in the market.
What will be the prevailing price in the market?
Compute the prot for each of the rms.
Compare the consumer surpluses between Question #6 and Question #7.
8. Prot function of a representative rm in a competitive market is given by = PQ wL rK F.
Here, P is the market price, Q is the output produced (sold), w is the wage rate, L is
the labor employed, K is the capital employed, r is the rental rate and F is the xed
cost that does not depend on the amount of quantity produced.
The rm uses a production function Q = AKL.
Algebraically solve for the prot maximizing labor (L) and capital (K) that the rm
should be using.
What is the total output produced by the rm? What is the prot earned by the rm?
Now assume that w = 15; = 0:4; = 0:5; A = 10; and P = 15.
Graph the prot maximizing labor (L) and capital (K) amounts when r increases
continuously from 1% to 5%.
(Use Excel to simulate as smooth an increase as possible. You may get quite a smooth
path if you plot the changes in r at one fth of one percent intervals).
Suppose this economy has 100 such rms. How will the total employment change as
the rate of interest inches up from 1% to 5%?
9. Find the best strategies for EACH player and carefully nd the Nash equilibrium of
EACH of the following games:
(Be careful about identifying pure strategy Nash equilibrium (equilibria). If
no pure strategy Nash equilibrium exists then check for the mixed strategy
Nash equilibrium)
(i)
Prisoner 2 ! Confess Dont Confess
Prisoner 1# Confess 18;18 2;20
Dont Confess 20;2 4;4
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(ii)
Country 2 ! Trade Dont Trade
Country 1# Trade 1000; 1000 600; 500
Dont Trade 500; 600 500; 500
(iii)
Intel ! cooperate Dont cooperate
Apple# cooperate 20; 20 13; 17
Dont cooperate 17; 13 18; 18
(iv)
Tax Payer Joe ! Cheat Dont Cheat
IRS# Audit (with Probability 0:5) 450;500 150;200
Dont Audit (with Probability 0:5) 0; 0 200;200
(v)
Applicant Russell ! Negotiate Dont Negotiate
Company X# O¤er a job 50; 40 60; 30
Dont O¤er a job 0;10 0; 0
(vi)
Player B ! Go to Opera Go to Movie
Player A# Go to Opera 1;1 1; 1
Go to Movie 1; 1 1;1
10. Prove that all Gi¤en goods are inferior goods but all inferior goods are NOT Gi¤en
goods. (A graphical proof will be su¢ cient).
11. When prices are (P1; P2) = (2; 4) a consumer demands (x1; x2) = (4; 2): When the
prices are (4; 2) the consumer demands (2; 4). Argue if the behavior of the consumer
is consistent with the utility maximizing behavior.
12. The total cost of a rm is given by C = 2 + 3Q + 4Q2 where Q is the total amount of
output.
What is the cost of producing zero units? What do you call this amount?
What is the total cost of producing four units? What is the marginal cost of producing
the fth unit? What is the marginal cost of producing the sixth unit?
Draw a graph depicting the following as the output rises from 0 to 100: MC, AVC,
ATC, AFC. (Tip: Use Microsoft Excel)
Looking at your answers, what can you say about the change in marginal cost as the
output level keeps increasing?
13. Suppose that the inverse market demand is given by P = 2005Q. Assume now that
the market is served by two rms (Cournot Model).
Marginal cost of production of rm 1, c1 is 5 and marginal cost of production of rm
2, c2 is 7. In other words, rm 1 is the low cost rm and rm 2 is the high cost rm.
Derive the following for this market:
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(i) equilibrium price (P)
(ii) equilibrium output of the rst rm (q1)
(iii) equilibrium output of the second rm (q2).
(iv) equilibrium total supply in the market (Q = q1 + q2)
(v) equilibrium output of the rst rm (1
)
(vi) equilibrium output of the rst rm (2
)
14. Consider the demand function of Question #13. Suppose the two rms are competing
in a leader-follower fashion (Stackelberg Model) where Firm 1 is the Leader and Firm
2 is the follower. Marginal cost of production of rm 1, c1 is 5 and marginal cost of
production of rm 2, c2 is 7. In other words, rm 1 is the low cost rm and rm 2 is
the high cost rm.
Derive the following for this market:
(i) equilibrium price (P)
(ii) equilibrium output of the rst rm (q1)
(iii) equilibrium output of the second rm (q2).
(iv) equilibrium total supply in the market (Q = q1 + q2)
(v) equilibrium output of the rst rm (1
)
(vi) equilibrium output of the rst rm (2
)
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