 आज हम प्रुदक्छन प्रबात करेंगे, प्रुदक्छन प्रुदक्छन is a very important tool, and with the help of this tool we will discuss the functioning of the economy. तो फर आप ये जान चुके हूंगे, के प्रुदक्छन is basically a relationship among different variables, and obviously production function is a relationship between output and the factors of production. आज हम एक बहुत ये सिंपल प्रुदक्छन प्रुदक्छन की बात करतें, के output is a function of labour. चिल करली की, करे थी बाआओई एक जान आप ये बाय करगते प्रुदक्छन प्रुदक्छन ख्या। जान प्रुद के साच्छ के ये भी खाँजनुर नफाँ सभर्ग करेंगे, की आप आप प्रुद के आप समझे नहीं। it depends how many units of workers have been utilized. So this was dataset for general forms, specifically we have different forms of reduction function. The most simple one is linear production function. So this example of linear production function is called en, a is some constant n is the units of workers. सो एकी वेल्य हों पाईव साईन कर हैं, पाईव आन मीन्स के नमबर वरकर्स को आप पाईव से मल्टिप्लाई करेंगे तो दिस फिल गेव युदा आमाच्ट अब अब अबट्बोट एक और इक देम्पल आम बाद करते हैं, नोन लिन्यर प्रोडक्षन फुंक्षन की ये भ प्रोडक्षन फुंक्षन जब हैं, इसो लेड़ाबरी कली के साज सात, ग्राफिक कली भी हम यस को दिसकराईप कर सेकते हैं, और अब प्रोड्षन प्रोडक्षन को अगर एस को विदाल्प ग्राफ डिसकर सकर नाचाईं, करना चाई, तो ये गराफ आपके सामने, होरिजन्टल ऐक्सिस पर we are taking the units of workers and on the vertical axis we are taking the units of output. तो ये जो स्टेट लाईन रेद आपको नधर आरी, तो ये स्प्रोडक्छन फूंशन को दिसक्राइब कर ये, that y is equal to 5m. तो अपका न दीए तो सताटिं पूँएग पूँएग तरीगा, थी कै ये क्या बतार है, कि न नमबर नबर कर लिजन्टल रेड जी़ है, तो जब आप ये प्रोडक्छन फूँँँँँँँँँँँँँँँँँँँँँँ, सो वो आपको वाई की वेल्यो देगी, आन की वेल्यो दीरो पूड करेंगे, तो 5 into 0 is equal to 0, so output is 0. अप्को लोग के जिस पान्त ए, तीके ए पर क्या है, नंबर वरकर दार 6, अप्पूड विल बी अखाडिंग तो this production function, 5 into 6 that is 30, so output will be 30 units. ये फिल्रा नाचना थी, ये वो पर और थी, लोग कि लिए नहीं च्डिए at f you can see number of workers are 10, and output will be 10 into 5, that is 50. एक घर उन गर तीग अब रहा सार डिखर सकर न चाह नहें, तो सलोब ये फुप रथ कि अन्ऻाई प्रच्छन और वो। अक्नामिक्स में सेलोप लोड़क्झन फुँशन कहाँ मालचन प्रुट्ट्ट, इंहाप औरेदेंतले क्सिस पर आपके पास लेपर है, सो सलोप लोड़क्चन प्रुट्ट्टचन वुशन गूँट्टिन बूद एक तो मालचन प्रुट्टट तो लेपर, इसको मैं का आज़े दीपार करेंगे, इसको में का आज़े दीपार करेंगे, यह आज़े आज़े थाई से थी तुब आप जा़नात्ते है, और गर पर जा़नाचा देदे थाई से वीगते है। नब यहन से एक की बिलनımızıि में जापते तो , if you go to point f, at f it contains 10 units of worker and we have for the cityawf workers that is on horizontal axis. And this vertical distance, delta y is giving us the change in the amount of output so, अब द्याच के हम वोगर ट्हाँ करें फakra from 6 to 10 that is we are adding 4 more workers and output is increasing from 30 to 50 that is output is increasing by 20 so, यन जारर करता लगा हूँ कोरी आप यता फलित्तें चे रव बलैनाोंसे कहात्ते आथ है वर जारने आलार अआथ है मेन लाहां बलगा possibile ज़ूँरTH ल्वाऔर के है वर्र ़ेक का अ Inteो धीट वर्गेस् थी कोरनी खौए, कौसोन करुक यहन्सेन tail of plejok नहीं, आदी ब ही ज़्रगते हैं। अब आन्ट लिनयर प्रब्रढचन् थी कँभी यगईंप यहांप ळैस कर लगते हैं।istas ka yai dikal to a and रेस तुपर लफा प्रभ्ब़बाद हैं। aa ki value hai, मैंगऊन की वural jo तो इसको हम दिसकस करते हैं, with the help of this graph. So, first of all, you can see again, we have on the horizontal axis, we are taking number of workers, vertical axis, we are taking output. और ये जो रेद आपको graph नदर आर है, तो ये बतार है, that first of all, it is non-linear, for reduction function, so the graph is non-linear. तो ये बतार है, that what relationship between number of workers and output. तो इसको अगर हम पोई जी सिफार इक देम पल हम सटाट करें, at g, अब देख सकते हैं, के वार करस कितन है, 1 and output is 20. कैसे जेस ताब ये इस परडक्षन फुंक्षन में, नहीं न परडक्षन फुंक्षन में, आनकी बेल्यु, 1 put करेंगें, under root of 1 is 1, तो 1 into 20, so 1 unit of output is giving us 20 units of output. And take another point, take this point d. At d, number of workers are 9 and according to this परडक्षन फुंक्षन, taking the under root of 9 that is 3, 3 into 20 that is 60, so 9 units of worker are giving us 60 units of output. So, if you join this point g with point d with the straight line, this black line we are joining point g with d, so the slope of this straight line will give you the average rate of change in y due to change in n. So, if you look at this, so 9 minus 1 that is 8 and 60 minus 20 that is 40, so 40 divided by 8 that when we move from 1 worker to 9 workers, then the output on average is changing by 5 units. Each additional unit of worker is giving us 5 units of output. Similarly, if you come to point c of d, so you see that change in y is 40 minus 20 that is 20 and number of workers change over 1 to 4 that is 3, so you divide 20 into 3, so this will give you another answer. And that answer will tell you about that how much in this region on average per unit of worker we are getting output. But as we move this d close to c and g, so if we want to know the slope of the slope in the very near neighborhood of g, then we draw a tangent for this graphically. This means a straight line which touches the point. So, the slope of this tangent line, this line is actually giving us the value of rate of change, instantaneous rate of change. Technically, we are saying this is the instantaneous rate of change that at very very near close neighborhood of point g. So, what is the rate of change of this? So, this is the product of labour. And you can see that when from c or d and when you are coming on the line of g and c, then this line is getting steeper and when you draw a tangent on c, then it is further, it has become steeper. So, you can say this in other words that as you are adding number of workers, the marginal product of labour is getting reduced. So, in this we have to carry two main things. First of all, slope of this production function is positive. This curve is going upward. I will show you again. So, you can see that this production function is going upward. Throughout, marginal product is positive. But second point is, look at the second point, that slope is becoming flatter and flatter. As we are moving, as we are increasing number of workers more and more, the marginal product of labour is decreasing. So, this is called diminishing marginal product. So, I hope this will help you to understand the next lecture. Thank you.