Problem Set 1
经济学问题集代写 1. Module 2: This question is based on your self-study of Chapter 2. Suppose that the demand for rental housing in Victoria is given by:
Econ 203
Kevin Andrew September 20, 2018
1.Module2: This question is based on your self-study of Chapter Sup- pose that the demand for rental housing in Victoria is given by:
Also suppose the supply of rental housing by landlords is fixed at:
QS = 1000 经济学问题集代写
Where price is in rent/month and quantity is number of apartments in a certain neighbourhood.
a)Represent demand and supply curves graphically with price on the vertical axis and quantity of housing on the horizontal axis. Clearly label the equi- librium point. What is special about the supplycurve?
b)Solve algebraically for the equilibrium quantity and price and check that it matches your diagram.经济学问题集代写
c)Calculate the consumer surplus, producer surplus and total surplus and show theseon your Hint: the consumer surplus is a triangle and the producer surplus is a square.
d)Now suppose that in an effort to make housing affordable the city of Victoria gives a subsidy of 100/month to all renters. This has the effect of shifting the effective demand curve to the right. Show the effects of this policy on your Hint: When you write your demand equation with priceon the LHS you will add $100/ month to the RHS.经济学问题集代写
e)Is the benefit from this subsidy shared at all between the renters and the landlords? Why or whynot?
f)Bonus Question: There is no dead-weight loss from this government in- tervention. Why do you suppose that is? Is this generally the case or specific to thiscontext?
2.Module 3: The Budget Line Suppose my grandma relates to me that when she was a little girl the only things she ever bought were candy and novels.经济学问题集代写
Her weekly allowance was $5 and the price of candy was $0.50/bag and the price of a novel was $2.50/book. For the sake of this problem assume it is okayto buy a fraction of a
a)Draw my grandma’s budget constraint with novels on the x-axis and candy on the y-axis. Interpret the slope and the intercepts of this line and clearly show what is affordable and unaffffordable.
b)What happens to the budget constraint if the price of candy doubles?Show this on your graph and interpret.
c)What happens to the budget constraint if the allowance doubles to $10/week? Assume the original prices of $0.50 and $2. Show this on thegraph.
d)Suppose that my grandma complains about how expensive novels and candy are these days. In fact, the price of candy has increased to $1/bag and the price of novels have increased to $5/book. However, a childs allowance isnow $10/week. Compare the modern childs budget constraint to my grandma’s? How might I explain the flaw in my grandma’s reasoning (nicely)?经济学问题集代写
e)BonusQuestion: Consider again the initial situation where allowance is$5/week and the price of candy is $0.50/bag. Suppose that my grandma got a loyalty card at her book store which said the price of the first book was$2.50 but after that the price was only $1.00/book. What will my grandma’s budget constraint look like now?
3.Module 4: Suppose that my preferences for hamburgers and hot dogs are given by:
U (x, y) = 2x + y
Where x is consumption of hamburgers and y is consumption of hot dogs.
a)Howmany hot dogs would I require to give up one hamburger and be “indif- ferent”.
b)What is the marginal rate of substitution between hamburgers and hot dogs? Howis this related to your answer in part a)?经济学问题集代写
c)Plot the indifference curvesfor:
U¯ = {2, 4, 8}
d)What is the equation for the indifference curve with y on the LHS and x on theright?
e)Supposeinstead that good y is the composite good and good x is Pref- erences are given by:
U (x, y) = y + √x 经济学问题集代写
Plot these indifference curves on a new graph for:
U¯ = {2, 4, 8}
f)What is the marginal rate of substitution for these new preferences? What is different about the MRS when compared to the preferences for hamburgers and hotdogs?
4.Module5: Suppose that demand for food and shelter is given by:经济学问题集代写
U (x, y) = x1/3y2/3
Where x is consumption of food and y is consumption of shelter. The price of food is $5/unit and the price of shelter is $20/unit. Income is $1, 000 per month.
a)Calculate the marginal rate of substitution between food and shelter.
b)Calculate the optimal choice of food and shelter at the given prices and income and represent it on a well labelled graph. Show the budget constraint, theoptimal choice as well as the indifferrence curve with x on the horizontal and y on the vertical axis.经济学问题集代写
c)Now solve for the demand “function” generally for x and y. Your solution should depend on prices and income.
d)Plot the individual demand curve for good x with quantity demanded on the horizontal axis and price on the vertical axis. Would the demand curve shift if the price of good y (shelter) wentdown?经济学问题集代写
e)Plot the Engel curve for good x with quantity demanded on the horizontal axis and income on the vertical axis. What is its slope? In this case is food (good x) a luxury or a necessity? Is it a normal or inferiorgood?
f)Bonus: The property that demand for good x is independent of the price of goody is very particular to the Cobb-Douglas Using a diagram and the concepts of income and substitution effects, explain why this is.
5.Module5: Suppose that my preferences for burgers and buns are:
U (x, y) = min{x, 2y}
a)Using simple language, explain what these preferences mean. For instance, talk about why you would want to consume burgers and buns in these fixed proportions(assume that 1 unit of buns is just a slice of bread).
b)Draw the indifference curvesfor:
U¯ = {1, 2, 3}
On a diagram with x on the horizontal axis and y on the vertical axis.
c)For each of the indifference curves above, show the budget line that is just tangent to it with px= py = 1. Draw the income consumption path.经济学问题集代写
d)Draw the Demand Curve for good x for these preferences. Does the price of good y shift the demand curve? In which direction? How is this related tothe special type of preferences we are dealing with?
e)What is the general demand equation for good y and good x? Hint: you cannotuse the marginal rate of Your answer should depend on income and the prices of good x and y.
f)Bonus: Suppose the price of hamburgers doubles. What will be the size of the substitution effect? Use a graph to illustrate.经济学问题集代写
g)Bonus: The income consumption path and the Engel Curve for these pref- erences were linear and increasing. Does this seem a reasonable outcome for mostgoods? Prove that this will not be the case for these preferences:
U (x, y) = y + ln x
6.Module6: Suppose there are 30 consumers in the market with preferences:经济学问题集代写
U (x, y) = x1/3y2/3
Assume x is the quantity of restaurant meals consumed and that y is the composite good.
a)What is the market demand curve as a function of income per person, M , and the price of good x? Hint: you have already solved these preferences in question 4). You may also use the Cobb-Douglas Rule tomake sure you are on the right track.经济学问题集代写
b)What is the price elasticity of market demand? What would happen to quan- titydemanded if the price of restaurant meals went up by 10%?
c)What is the income elasticity of demand? What would happen to quantity demanded if income rose by25%?
d)Now suppose that in addition to the original 30 consumers there are 30 con- sumers withpreferences:
U (x, y) = min{x, y}
What is the market demand curve now? Hint: the individual demand for good x is x = M x y with these preferences.经济学问题集代写
e)Take the derivative of market demand with respect to py. Are goods y and x substitutesor complements at the level of the market?
f)Bonus: When income is 100 and px= 1, py = 1 and M = 100 what is the price elasticity of market demand? In this case is demand elastic or inelastic?
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