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To produce one unit of commodity X requires only half a unit of labour (no capital is needed). Each unit of X needs storage space during the production process which is limited to up to 180 units of X. Commodity Y, on the other hand, requires a quarter of a unit of labour and half a unit of capital for the production of one unit. There are 100 units of labour and 100 units of capital. a) Draw the production possibility frontier. b) What will be the opportunity cost of Y when we produce 30 units of it? c) What will be the opportunity cost of X when we produce 80 units of it? d) Had we produced

OCW Scholar - Principles of Microeconomics
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I have just started studying economics(micro) on my own. Here is my attempt. Let us first calculate maximum units of X and Y produced from with given resources and constraints. i) Maximum units of X produced ( this is 180 units) With 100 units of labor(no capital required) 200 units of X can be produced (Now this is above 180 units constraint that the storage forces) . So only, 180 units of X can be produced and for that 90 units of Labor is required Now we have 10 units that is not utilized to produce X , it can be used in production of 40 units of Y (a unit of Y requires 1/4 unit of labor). ii) Maximum units of Y produced (this is 200 units) With 100 units of labor and 100 units of capital : Since more capital is required to produce Y as compared to labor , whole units of labor will not be used. You can only combine 50 units of labor with 100 units of capital at maximum and that will give you 200 units of Y. 50 units of labor is not utilized here and that can be used to produce 100 units of while producing maximum Y. Now , Back to questions b) What will be the opportunity cost of Y when we produce 30 units of it? There is no opportunity cost involved . Since we can produce Maximum of X while producing 30 units of Y. Until we are producing more that 40 units of Y , no opportunity cost is involved .Because till 40 units of Y we can produce maximum X. c) What will be the opportunity cost of X when we produce 80 units of it? In the came vain, no opportunity cost is involved here also. Till 100 units of X we can produce maximum units of Y and 80 units is less that 100 units. d) Had we produced? I really didn't get this question. What is the context? produced what and when? If it means to ask have we produced Y when producing maximum X and vice-verse, then yes ,of course, we have produced. Hope I am correct and this helps .
I had some problem uploading the attachment in the morning for question a)

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