MODULE CODE: MATH0002
ASSESSMENT PATTERN: MATH0002A4UA
MODULE NAME: Economics 1(Combined Studies)
LEVEL: Undergraduate
DATE: 08 May 2019
TIME: 14:30
TIME ALLOWED: 3 hrs
SUMMER TERM 2019
MATH0002:Economics I(Combined Studies)
TIME ALLOWANCE:3 hours
Ansqner ALI questions from Part A, ONE question from Part B,and ONE question from Part C. Correct butunerplained answers will not receive high marks.
Questions in Part A carry five percent of the total mark each,and questions in Parts B and C carry twenty-five percent of the total mark each.
In cases where a student answers more questions than requested by the eramination rubric,the policy of the Economics Department is that the student's first set of answers up to the required number will be the ones that count (not the best answers).All remaining answers will be ignored.
PART A
Answer ALL questions from this section.
A.1 Suppose that the supply function for Happyland's medical services is Qs(p)=p,where p is the price of medical services in f per unit.If citizens'demand for medical services is then what are the equilibrium price and quantity demanded by citizens only?If the demand function of foreigners living in Happyland is ,then what is Happyland's total demand function,Qp(p),for medical services?By considering the overall demand for medical services from both citizens and foreigners,what are the overall equilibrium price and quantity demanded for medical services in Happyland?
A.2 Suppose that the market demand for an economics textbook is given by Qp(p)=100-2p,where p is the price of the economics textbook measured in f per unit.Let the market supply function for this textbook by given by Qs(p)=3p.What is the market price and number of textbooks demanded at equilbrium?Suppose now that the government is considering a E5 specific tax per unit sold to be collected from sellers,by how much would the price consumers pay change?How much tax revenue would be collected?What fraction would be paid by sellers?
A.3 The Slutsky equation with an exogenous income is ,where x and hr are Marshallian and Hicksian demands,respectively,pr is the price of the good,and m is the exogenous income.What is the sign of If the good is normal,then what happens to its quantity demanded as its own price decreases,ceteris paribus?Now,suppose that income is endogenous,which means that the Slutsky equation is adjusted to account for the endowment of good x,Wz,as follows: .For a normal good,does the endowment effect reinforce or oppose the income effect?Explain your answer intuitively by using a diagram that decomposes the substitution,income,and endowment effects.
A.4 A firm manufactures output,q,according to the production function f(L,K)=LI/2Kl/2,where L and K indicate the input of labour and capital,respectively.Find the optimal amount of each input to use and the resulting cost function,C(q),given the wage rate,w=4(in E/unit labour), and rental rate,r=1(in f/unit capital).Using the Lagrange multiplier,determine the increase in the minimised cost if the production target,q,is increased by one unit.Verify your answer by differentiating the cost function,C(q),to obtain the marginal cost.
A.5 Assume that industry inverse supply and demand functions for a particular good are p=Q and p=10-Q,respectively,where p is the price of the good and Q is the quantity demanded or supplied.Calculate the deadweight loss associated with a EG per unit price floor provided by the government on the good.
A.6 What is the money multiplier and what factors determine its size?Obtain the expression for the money multiplier under the assumption that people hold currency and checkable deposits.
A.7 The labour force participation rate in the U.S.increased steadily from the late 1950s tntil mid- 2000s.First,briefy explain what the participation rate represents.Second,explain how the presence of discouraged workers affects the participation rate.Third,explain why the partici- pation rate has increased.
A.8 Based on your understanding of the aggregate supply and aggregate demand model and the IS-LM model,graphically illustrate and explain what effect a decrease in the money supply will lave on the economy.In your graphs,clearly illustrate the short-run and medium-run equlibria.
A.9 Derive the expectations-augmented Phillips curve and explain how it differs from the original Phillips curve.
A.10 Derive the uncovered interest rate parity and briefly discuss the assumptions behind it.Explain what a “sudden stop”is and how it is related to uncovered interest parity.
PART B
Answer ONE question from this section,i.e.,either B.1 OR B.2.
B.1 A consumer can buy two goods,X andY.Her utility function is U(X,Y)=xty.The prices of the two goods are px =1 and py =2(both in f per unit),and her exogenous income is m=100(in f).
(a)Solve the consumer's utility-maximisation problem to obtain the optimal consumption bun- dle and maximised utility level.
(b)Repeat part(a)with a different price for good X,p/x =2.
(c)What should be this consumer's adjusted income,m',so that her original optimal consump- tion bundle from part (a)is just affordable under the prices given in part (b)?What will be the consumer's maximised level of utility with adjusted income m and prices p/x =2 and py =2?
(d)How much minimum extra income should be given to the consumer under prices px =2 and py=2 so that her maximised utility is equal to that in part (a)?
(e)What kinds of income adjustments are offered in parts(c)and (d)?Which one of the two is a true cost-of-living adjustment (COLA)?Discuss why consumer price index (CPI) adjustments may be preferrable to use in practice,e.g.by governments.
B.2 The industry demand function for a particular good is D(p)=24-p,where p is the price of the good (in f/unit)and D(p)is the industry-wide quantity demanded.Initially,imports are banned,and there are n =6 identical domestic firms in this perfectly competitive industry,each with cost function C(q)=9+q²,where q is each firm's output.
(a)Determine the average cost,average variable cost,and marginal cost of each firm.
(b)What is each firm's short-run supply curve in terms of output price per unit,p?What is the industry short-run supply curve,S(p)?
(c)Find the equilibrium price and quantity consumed in this industry.Calculate the consumer surplus,producer surplus,and total surplus.
(d)Suppose that imports are now allowed.The supply function of foreign producers is Sr(p)= 2p.What is the total industry supply curve,Sr(p)?Using this,calculate the new equilib- rium price and quantity consumed along with the consumer surplus,producer surplus,and total surplus.What is the level of imports?
(e)Instead of allowing unlimited imports,suppose now that the government imposes an import quota of 6 units.Is this quota binding?Determine the new total industry supply curve with this quota, ).What are the new equilibrium price,quantity consumed,consumer surplus,producer surplus,and total surplus?
PART C
Answer ONE question from this section,i.e.,either C.1 OR C.2.
C.1 Consider an open economy characterized by the equations below.
C=co+c₁(Y-T)
I=do+d₁Y
IM = m₁Y
X =x₁Y*
The parameters m1 and xi are the propensities to import and export.Assume that the real exchange rate is fixed at a value of 1 and treat foreign income,Y*,as fixed.Also assume that taxes are fixed and that government purchases are exogenous (i.e.,decided by the government). We explore the effectiveness of changes in G under alternative assumptions about the propensity to import.
(a)Write the equilibrium condition in the market for domestic goods and solve for Y.
(b)Suppose government purchases increase by one unit.What is the effect on output,ie.what is △Y?(In your analysis assume O
(c)Calculate the change in exports(△NX)when government purchases increase by one unit.
Now consider two economies:one with m1=0.5("the small economy")and the other with μ1=0.1(“the large economy”).Assume that in each economy ci+d1=0.6.
(d)First comment on why the large economy should have a relatively smaller m₁.Then cal- culate your answers to parts(b)and (c)for each economy by substituting the appropriate parameter values
(e)In which economy will fiscal policy have a larger effect on output?In which economy will fiscal policy have a larger effect on nel exports?Provide the economic intuition behind your results
C.2 You are asked to model unemployment in an economy with search frictions.Suppose that unemployed workers move into jobs at a rate f,which depends on the number of job vacancies (v),a job search effectiveness parameter(i),and an index of skills mismatch(mm).Employed workers,on the other hand,lose their jobs at a rate s and that the labour force L is,for the moment,constant.
(a)Obtain an expression for the evolution of the unemployment rate u over time.Derive from this the steady-state unemployment rate and describe how the relationship between the unemployment rate and the number of vacancies leads to the Beveridge curve.
(b)Explain how u determines the number of vacancies created through the labour market,i.e. explain the rationale behind the job creation curve.
(c)Suggest two possible factors that may cause the Beveridge curve to shift outwards and briefly explain your reasoning.
(d)What would be the impact of a rise in unemployment benefits?Show the results graphically along with a brief explanation in words.
(e)Now suppose that due to the ongoing uncertainty in the domestic economy,skilled workers leave the country,causing the labour force to decrease at a rate a.In other words,assume that and that individuals are employed when they decide to leave.If α =1%, s=1%and f=8%,obtain a new expression and the resulting value for the steady-state unemployment rate.Using your model explain the impact of a on u.