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penn101_09s_hw3sol

# penn101_09s_hw3sol - Intermediate Microeconomics(Econ 101...

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Intermediate Microeconomics (Econ 101) Spring, 2009 Solutions to Additional Problems in Assignment 3 Solution to Question 1. (1) Notice we have a unit elasticity demand function for wool production, p = - 1 which implies - 1 = Δ q q Δ p p Δ p p = - Δ q q . That is, a percentage change of price will induce the same percentage change in the opposite direction of quantity demanded. Since Australian wool production accounts for 1 2 of the world production, an increase of 1% of Australian wool production will cause the world wool production to increase by .5%. In order for the demand side to absorb the extra quantity, price needs to fall by .5%. (2) Let ¯ q denote the initial level of the world’s wool production level. Australia can only control their own production, while the rest of the world’s wool production is fixed at . q . Let q a be Australia’s wool production. Then from Australia’s perspective, the world’s wool production is q = . q + q a , and the inverse demand function it faces is: p = A q = A . q + q a . The total revenue to Australia from wool sale is given by the equation R = q a p . The marginal revenue to Australia is: MR = dR dq a = ∂R ∂q a + ∂R ∂p dp dq a = p + q a dp dq a . Using the inverse demand function for Australia, we get: dp dq a = - p . q + q a = - p q . Plug dp dq a = - p q into the expression of MR , we get: MR = p + q a ( - p q ) = p (1 - q a q ) . Thus, holding the rest of the world wool production constant, the marginal revenue to Australia is the world price of wool times the complement of Australia’s market share of wool production. At q a = ¯ q , the marginal revenue to Australia is 50% of the price. Notice the marginal revenue to Australia is a decreasing function in its wool production.

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penn101_09s_hw3sol - Intermediate Microeconomics(Econ 101...

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