economics question1

8/19/2019 Economics Question1

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ECON5502

Midterm Study Guide

BRIEFLY DEFINE THE FOLLOWING CONCEPTS:

1. Mixed strategies and pure strategies

2. Normal form and extensive form games

3. Cournot-Nash equilibrium

4. Network externality

5. Evolutionary Game

6. Circulating capital model

7. Pareto efficiency

SHORT A NSWERS

1. In the Hawk-Dove Game players compete for a prize, represented here as the payoff

100. Each player adopts a strategy described as either Hawk or Dove. When a Hawk

meets a Hawk, they fight and damage each other and the prize. When a Hawk meets a

Dove, the Dove retreats and gets nothing, while the Hawk carries off the prize. When a

Dove meets a Dove, they divide the prize. The Hawk-Dove Game can be described by the payoff matrix:

A(row)/B(column) Hawk Dove

Hawk -20,-20 100,0

Dove 0,100 50,50

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a) What are the Pareto-efficient outcomes? (Explain your reasoning.)

b) What are the best responses? What are the Nash equilibria?

c) Are there any dominant strategies? If so, which?

d) What are the conflict and common-interest elements in this game?

e) What general type of social coordination problem does this game represent?

2. Consider the interaction between Toyota and Honda in their decision to expand their

capacity. Suppose that each firm has three strategies: Do not build, build a small plant,

or build a large plant. The payoff matrix is:

Toyota(rows)/Honda(columns) Build Large Build Small Do Not Build

Build Large 0,0 12,8 18,9

Build Small 8,12 16,16 20,15

Do Not Build 9,18 15, 20 18, 18

a) What are the Nash equilibria?

b) Is the Nash equilibrium Pareto efficient?

c) What are the Pareto efficient outcomes?

3. Consider a capitalist corn economy in which one year of one worker’s labor plus 6

bushels of seed corn yield 10 bushels of corn one year later. In this economy land is

free and wages are paid at the beginning of the year. We can represent this technique

of production by:

6 bushels of seed corn⊕1 year labor→ 10 bushels of corn

a) Find the wage-profit relation for this economy. What is the profit rate if the wage

is 1 bushel of corn per year per worker? What is the maximal rate of profit? What

is the maximal wage?

b) Assume workers consume all of their wages. What must the growth rate of the

corn stock be if capitalists re-invest all of their profits? What must the growth rate

of the corn stock be if capitalists consume half of their profits?

c) Suppose a new technique of production becomes available that allows 15 bushels

of corn to be produced per worker year while using 10 bushels of seed corn.

10 bushels of seed corn⊕1 year labor→ 15 bushels of corn (0.1)

If this new technique is adopted wile the wage is constant at 3 bushels what is the

new profit rate? Would a profit maximizing capitalist adopt this technique if she

instead faced a wage constant at 2 bushels?

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4. Consider the production function:

f [x 1,x 2]= (x ρ

1 +x ρ

2 )1ρ , with −∞ 0 (0.4)

a) Calculate the profit-maximizing demand and supply functions.

b) Show that the conditional factor demand functions are homogeneous of degree

zero in input prices.

c) Use these functions to calculate the profit function.

d) What restrictions must a and b satisfy?

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economics question1

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