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ASSIGNMENT ECF 410: ADVANCED MICROECONOMICS QUESTION ONE (10 MARKS) a) Write short notes on the following terms as used in microeconomics

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ASSIGNMENT

ECF 410: ADVANCED MICROECONOMICS

QUESTION ONE (10 MARKS)

a) Write short notes on the following terms as used in microeconomics.

i. Game theory

ii. Consumer preference

iii. The most we can say about the Demand Curve is that it slopes down unless it slopes up. Discuss.

b) Critically examine properties of ordinary demand functions

c) Distinguish between a production function and a production set

d) Suppose that ?(?₁, ?₂) = (xⁱ₁ + xⁱ₂)^1/i generate the associated cost function

QUESTION FOUR (10 MARKS)

Suppose that the market demand and cost of duopolist is given by

? = 100 − 0.5(?₁ + ?₂)

?₁ = 50?₁

?₂ = 0.5q₂

i. Derive the reaction curves of the duopolist

ii. Find the stackelberge solutions for each firm and the total output in the market

iii. What price will be charged by the duopolist

QUESTION SIX (10 MARKS)

An industry with two firms 1 and 2 is analyzed and the following cost functions C₁(x₁) = 5_x1 and C₂(x₂) = 0.5x²₂. Market demand is given by p = 10 – (x₁ + x₂).

i. For the Cournot duopoly, find the market equilibrium (price p and quantity ? = ?1 + ??2), individual supply and profits of both firms.

ii. How would the equilibrium price and individual supply change if firm 1 could reduce its marginal costs by 20%?

iii. What is the welfare effect of this cost reduction?