Question

What is the range for the relative price of cloth such that the economy produces both cloth and food? From _______ to _______ . Which good is produced if the relative price is higher than this range?

Answer 1

The answer is explained in detail below

Explanation:

$a_{KC} = 2$

$a_{LC} = 2$

$a_{KF} = 3$

$a_{LF} = 1$

Labor, L = 2000; Capital, K = 3000  

Labour constraint,

$2Q_{c} + Q_{F} \leq 2000$

Capital constraint ,

$2Q_{c} + 3Q_{F} \leq 3000$  

Solving the equation further, we get

$Q_{F} \leq 2000 - 2Q_{C}$

$Q_{F} \leq 1000 - \frac{2}{3} Q_{C}$

• The range for the relative price of cloth such that the economy produces both cloth and food is  2/3 and 2

• Low cloth production → economy will use relatively more labor to  produce cloth → opportunity cost of cloth is 2/3rd units of food.
• High cloth  production → economy dips on labor → taking capital away from food  production → raising opportunity cost of cloth to 2 units of food.  

• If relative price of cloth lies between 2/3 and  2 units of food, the economy  produces both goods.
• If the price of cloth decreases below 2/3 → complete  specialization in food production → low compensation for producing cloth
• If the price of cloth  rises above 2 → complete specialization in cloth production → low compensation for producing  food