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Assignment 2 - ECON 281 B1

2022

1 TRUE, FALSE, UNCERTAIN Questions

Argue with math, graphs and logical reasoning. All points will be awarded for your argument.

Question 1.[10pt] The marginal cost curve always intersects with the average cost curve at the average cost curve's minimum.

Question 2.[10pt] The market for PC video games is (almost) perfectly competitive.

2 Production Functions

Question 3.[20pt] Consider the following production function

where A is technology, L is labour, and K is capital. a is a positive constant.

a) Derive the average productivity of labour and capital.

b) Derive marginal productivity of labour and capital.

c) Derive the returns to scale of this production function.

d) Derive the marginal rate of technical substitution (MRTS) and the elasticity of substitution a.

e) Which kind of technological progress does A represent? Why?

3 Economic Cost Short Run Equilibrium

Question 4.[15pt] Consider the following production function

Q = 50L + 25K

assume that the cost of capital and labour are r = 9, w = 20.

a) Sketch some iso-cost lines and the isoquant for a production target of Q = 1000.

b) Set up the minimization problem and derive the firm's optimal labour and capital input

c) Derive and draw the firm's total cost curve

d) How does your answer change if both input prices double (input demands and cost curve)?

Question 5.[20pt] Consider the following production function

F (K,L) = AL¹K¹,

where A = 2,/t = 8,r = 4,w = 16.

a) Derive the short-run demand for labour when capital K is fixed at K.

b) Derive and sketch the short-run total, variable and fixed cost function.

c) Derive and sketch the firm's marginal and average cost.

d) What is the firm's shut-down price?

e) What is the firm's break-even price?

f) What is the firm's individual supply?

g) Assume consumer demand is given by Q^D = 90 — P. What will be the equilibrium market price and quantity when there is a total of 20 identical firms in the market?

h) What is an individual firm's profit at this price? Is this equilibrium sustainable? What will happen in the long run (in words)?

4 Long Run Equilibrium

Question 6.[15pt] Consider the same production function as in question 8, but now in the long run

F (K,L) = AL 1 K 1,

where A = 2,r = 4,w = 16.

a) Derive the long-run input demand for labour and capital using the MRTS and input price ratio.

b) Derive and sketch the long-run total, marginal and average cost.

c) Determine the long run market price.

d) Assume consumer demand is given by Q^D = 90 — P. What will be the equilibrium market quantity?

e) Can you determine the optimal number of firms and output per firm? What is the problem?

Question 7.[10pt] Consider the following long run cost function

TC (Q) = 40Q + 2Q² + 288,

market demand is

D(P) = 356 — 2P

a) Determine optimal production per firm using both methods learned in class

b) Determine equilibrium price and verify that profits are zero

c) Determine the optimal number of firms and sketch market supply and market demand.

What is the equilibrium quantity supplied in the market?