Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q=min{L/3, K0.5}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q=2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. b) Let the price of labour-hour be given w = $18 and the price of fruit by p = $5 per kg. What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of kiwi? d) What is Cheburashka's long-run total cost function, C(q), for w= $18 and p = $5? Sketch it on a graph. e) Cheburashka currently produces 20 bottles of juice. Given the economic conditions, he expects wages to start increasing, but, luckily, the price of kiwi to stay the same. One of Cheburashka's advisers, Madam Shapoklyak, suggests that if the wage keeps increasing as predicted, he should hire less labour and use more kiwi fruits to minimise costs (to produce the same 20 juice bottles). Briefly evaluate the quality of her advice. (If you agree with her advice, explain why; if you disagree, please explain why, and suggest an alternative.)
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q=min{L/3, K0.5}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q=2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. b) Let the price of labour-hour be given w = $18 and the price of fruit by p = $5 per kg. What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of kiwi? d) What is Cheburashka's long-run total cost function, C(q), for w= $18 and p = $5? Sketch it on a graph. e) Cheburashka currently produces 20 bottles of juice. Given the economic conditions, he expects wages to start increasing, but, luckily, the price of kiwi to stay the same. One of Cheburashka's advisers, Madam Shapoklyak, suggests that if the wage keeps increasing as predicted, he should hire less labour and use more kiwi fruits to minimise costs (to produce the same 20 juice bottles). Briefly evaluate the quality of her advice. (If you agree with her advice, explain why; if you disagree, please explain why, and suggest an alternative.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Hi I need help with part e
Transcribed Image Text:Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function
is:
q=min{L/3, K0.5},
where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example,
if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice.
a) Draw isoquants for q = 1, q=2 and q = 3 on a graph with labour on the horizontal axis and
kiwi fruits on the vertical one.
b) Let the price of labour-hour be given by w = $18 and the price of fruit by p = $5 per kg.
What is the optimal amount of labour and fruit to produce q bottles of juice if
Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q)
and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines.
c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the
expansion path, i.e., K as a function of L. How does it depend on the wage and the price of
kiw
d) What is Cheburashka's long-run total cost function, C(q), for w= $18 and p = $5? Sketch
it on a graph.
e) Cheburashka currently produces 20 bottles of juice. Given the economic conditions, he
expects wages to start increasing, but, luckily, the price of kiwi to stay the same. One of
Cheburashka's advisers, Madam Shapoklyak, suggests that if the wage keeps increasing as
predicted, he should hire less labour and use more kiwi fruits to minimise costs (to
produce the same 20 juice bottles). Briefly evaluate the quality of her advice. (If you agree
with her advice, explain why; if you disagree, please explain why, and suggest an
alternative.)
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