Econ 3T03
Fall 2010
Home Assignment #5: Answer Key.
Show all your calculations and explain all your answers
1. (6 points.)
The economy of Hogwarts produces magic potion using lemon grass (
G
) and troll labor (
L
),
and a constant return to scale technology. Total output is growing at the rate of
6%
per year. The troll’s wage
is
1
bottle of magic potion. The troll labor output ratio is
1:4
. The stock of lemon grass and troll population
are growing at the ratios of
4%
and
3%,
respectively. Assume that every troll works.
(a) If all output is paid in wages to trolls and cost of lemon grass (in other words, the total cost of magic
potion production equals to the output, where you can denote by r the price of 1 pound of lemon grass),
calculate the shares of lemon grass and troll labor in Hogwarts’ income.
(b) Estimate the rate of technical progress (or TFP growth) in Hogwarts.
(c) Suppose that doubling the inputs results in
2.5
times the original quantity of magic potion. How does this
affect your answer to part (b)?
(d) Suppose that only one third of troll population is engaged in production at any date. How does this affect
your answer in part (b)?
Answer: we need to use the TFP growth equation to solve this problem
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 Fall '10
 demidova
 Economics, 3%, Tax avoidance and tax evasion, 1 pound, 0.75%, 2.25%

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