ECON 357 Assignment 2, Version A
100 marks
Each question is worth 15 marks with the exception of
question 6, which is worth 10 marks.
1. Given the
following production function: q = 10KL
a) If w =
25, r = 75, and C = 1200, mathematically find the minimum cost combination of
capital and labour to produce a given level of output.
b) Does the
production function in part (a) show increasing returns to scale, decreasing
returns to scale, or constant returns to scale?
Explain.
c) Using
isoquants and isocosts, graphically illustrate the effect of an increase in the
wage rate (assume the firm is producing at the same level of output).
2. Given the
following total cost function facing a perfectly competitive firm:
TC = 500 + 10q2
a) If price
= 100, determine the level of output and profit earned by the firm in the
short-run.
b) Based on
your answer for part (a), should the firm continue to produce in the
short-run? Why or why not?
c) Graphically
illustrate a perfectly competitive firm earning a positive profit, zero profit,
and incurring a loss in the short-run.
3. Given the
following inverse demand and supply functions:
P = 40 – 2Q
P = 10 + 3Q
(a) Determine
the equilibrium quantity and the equilibrium price.
(b) If the
government imposes a $10/unit tax on the seller, determine the after tax
equilibrium quantity and price. How much of the tax is paid by the seller and
the buyer?
(c) If the
government now imposes a $10/unit tax on the buyer instead, determine the after
tax equilibrium quantity and price. How
much of the tax is paid by the seller and buyer?
?
4. Given the
following information for a monopolist:
P = 40 – 2Q
TC = 4Q + 4Q2
(a) Determine
the profit-maximizing level of output and price charged by the monopolist.
(b) Determine
the profit level.
(c) Graphically
illustrate a monopolist earning a profit in the short-run.
5. To
increase profits, a monopolist has decided to engage in third-degree price
discrimination by separating its customers into two groups and charging
different prices for each group.
a) What type
of price discrimination is the firm planning to engage in? Graphically illustrate the effect on price
and output for both groups of customers.
b) Given the
following two demand functions and
overall marginal cost, determine the output produced and price charged for each
group:
P = 2000 – 5Q
P = 100 – Q
MC = 10
c) Compare
the results from part (b) between the two groups.
6. Marge’s
Beauty Salon sells shampoo and conditioner. Marge has two types of
customers. Their willingness-to-pay for
shampoo and conditioner are given in the table below. If Marge bundles the
shampoo and conditioner, could she increase revenue? Show your calculation.
Shampoo Conditioner
Type I 8 5
Type II 6 8
7. a) Assuming competitive factor markets,
graphically illustrate and explain the difference between marginal revenue
product for a competitive output market and a monopolistic output market.
b) Assuming
competitive factor markets, graphically illustrate and discuss the effect of an
increase in the wage rate in a competitive labour market.
c) Graphically
derive the long run demand curve in a competitive factor market and explain the
underlying theory.
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