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National University of Singapore EC2101 Microeconomic Analysis I

Department of Economics Semester 2 AY 2012/2013

1

Homework

2

Production, Costs, and Short-Run Perfect Competition

Due date: 5 Apr 5 pm

Question 1 Answer the following questions. Briefly explain your answer.

a) You obtained the following short-run cost information of a firm. When the firm

produces 2 units of output, its total cost is $500,040. When the firm produces 10 units

of output, its average fixed cost is $50,000. What is the average fixed cost when the

firm produces 2 units of output? What is the average fixed cost when the firm

produces 5 units of output?

b) A profit-maximizing firm in a perfectly competitive market currently produces at

an output level where its short-run average total cost curve is upward sloping. What

does this imply about the firm’s economic profit?

Question 2 A firm produces a product with labor and capital. The price of labor is

w=2, and the price of capital is r=1.

a) Suppose the production function is q= LK . What is the equation of the long-run

total cost curve? Suppose in the short run, capital is fixed at K=4, what is the equation

of the short-run total cost curve?

b) Suppose the production function is q= L+K . What is the equation of the long-run

total cost curve? Suppose in the short run, capital is fixed at K=4, what is the equation

of the short-run total cost curve?

c) Suppose the production function is q= min(2L,K) . What is the equation of the

long-run total cost curve? Suppose in the short run, capital is fixed at K=4, what is the

equation of the short-run total cost curve?

Question 3 A firm has production function q=2LK +K . The price of labor is w=1

and the price of capital is r=1. (L and K do not have to be integers.)

a) Suppose in the short run, capital is fixed at K=5. What is the equation of the short-

run total cost curve?

b) In the long run, what is the cost-minimizing input combination when the firm

produces q=18? What is the level of total cost at this input choice?

c) Suppose now w=8 and r=1. What is the long-run cost-minimizing input

combination when the firm produces q=3? What is the level of total cost at this input

choice? Suppose in the short run, capital is fixed at K=1. What is the level of total

cost in the short run if the firm produces q=3?

National University of Singapore EC2101 Microeconomic Analysis I

Department of Economics Semester 2 AY 2012/2013

2

Question 4 In a perfectly competitive industry, every firm has identical cost structure.

The short-run total cost curve of an individual firm is STC(q)=40+10q+0.1q2.

Currently there are 10 firms in the market. The market demand curve is D(P)=700-

10P.

a) What is the equation of an individual firm’s short-run supply curve?

b) What is the short-run equilibrium price and quantity in this market?

c) At the equilibrium, what is the total producer surplus in the market? What is the

profit of an individual firm?

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