代写 Econ 100 – Assignment

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Econ 100 – Assignment 1 Winter 2017

TAnswer each of the following

questions. You must provide justification to receive marks. Students may collaborate in solving

the problems but must individually write up their answers.

Question 1. Consider a country with L = 100 units of labour per period to allocate between the

production of good 1 and good 2. The amount of labour used in producing good 1 is L1, and the

amount used in producing good 2 is L2. The production relationships are represented by �1 = (�1)1/2 ��

i) Use the constraint on the use of labour and the production functions above to

derive the production possibilities function (relating feasible output levels of the two

goods).

ii) Find the expression for the marginal rate of transformation in terms of the first

good.

iii) Sketch the production possibilities frontier with the first good measured horizontally

and the second good measured vertically.

iv) If the country always prefers to have equal amounts of the two goods in the largest

quantity possible, how much will it produce of the two goods?

v) Suppose the country can trade its goods in an international market where the price

of the two goods are equal. Show graphically that the highest level of consumption

with �1 = �2 will occur when ��(�1) = −�1

vi) Find the production and consumption levels of the country under the assumptions in

v).

vii) Illustrate the outcome of the country in your graph in iii) (or redraw the figure and

add the result).

Question 2. Suppose there are three households and 6 firms participating in a competitive

market for a commodity.

i) If the household demand functions are

Find the market demand function q(p) by summing individual demands over relevant intervals

of prices.

ii) Sketch the market demand curve representing the quantity demanded horizontally

and the price of the commodity vertically.

iii) Suppose the 6 firms individually have the same supply function,

�1(�) =

Find the market supply function and add it to your sketch in ii).

iv) Find the market equilibrium price and quantity using your graph in iii) to guide your

reasoning.

Question 3. Suppose the market demand for a commodity is given by

i) At what point (q, p) on the demand curve is the price elasticity of demand

equal to one in absolute value?

ii) Over what values of quantity demanded will a fall in the price lead to an

increase in the revenue generated in the market?

iii) Suppose the market supply function is s(p) = p/2. What are the equilibrium

price and quantity?

iv) If the government adds a tax of $t/unit, what will the equilibrium quantity be

in terms of t?

v) If tax revenue is t times quantity traded, use your result in iv) to find the best

choice of t for the government.
代写 Econ 100 – Assignment