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

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

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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