# UNKNOWN 800 Assignment 4 – In the Long Run equilibrium

April 10, 2017

Subject: Economics    / General Economics

Intermediate Microeconomics 73-230:
Assignment #4

Question
Points
Score 1
15 2
15 3
10 4
20 5
20 Total
80

Intermediate Microeconomics 73-230: Assignment #4 Problem 1
1.a In the Long Run equilibrium, for each identical firm in a perfectly competitive industry:
(A) Marginal Cost=price
(B) Marginal Cost=average total cost
(C) Profit ? = 0
(D) All of the above are true
1.b In short-run a firm will produce if and only if:
(A) p = M C
(B) p ? min AV C
(C) ?(q) ? 0
(D) All of the above are true
1.c Draw a graph showing the average total cost, average variable cost, and marginal cost curves for a
typical firm. On your graph, draw in three prices: label as P3 a price that results in the firm making
positive profits; label as P2 a price that results in the firm breaking even; and label as P1 a price that
results in the firm making negative profits that are less than fixed costs.

Intermediate Microeconomics 73-230: Assignment #4 Problem 2
Suppose that a perfectly competitive firm’s total cost of producing output q is T C(q) = 10+10q ?q 2 +0.25q 3
and market price p? = 10.
2.a Find the short-run supply curve of a firm in this industry. 2.b How much will the firm produce at p? = 10?

Intermediate Microeconomics 73-230: Assignment #4 Problem 3
A firm’s production function is:
F (L, K) = min(4K, 2L)
Sketch the firm’s isoquant map.

Intermediate Microeconomics 73-230: Assignment #4 Problem 4
Recall the definition of Returns to Scale (e.g. for all ? &gt; 1) from class. In the following exercises I want you
to think about returns to scale for Cobb-Douglas and CES (Constant Elasticity of Substitution) production
functions. For the followings, justify whether the production function is Constant, Increasing or Decreasing
Returns to Scale and derive the marginal products of labor M PL and of captial M PK .
4.a Cobb-Douglas F (L, K) = 20K 1/3 L1/6 4.b CES F (L, K) = (K 1/2 + L1/2 )2

Intermediate Microeconomics 73-230: Assignment #4 Problem 5
Consider a perfectly competitive industry. Each (identical) firm has the following total cost function
C(q) = 16 + 4q 2
The market demand facing the industry is as follows
Qd (p) = 500 ? 10p
where p is the market price.
5.a What is the long run equilibrium individual firm’s profit ? ? ? Show your work. 5.b What is the long run equilibrium market price p? ? Show your work. 5.c What is the long run equilibrium individual firm’s quantity q ? ? Show your work. 5.d What is the number of firms in the industry N ? ? Show your work. Page 5 of 5

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