 दलेबर मार्किट, जी सुडन्त आज हम बात करेंगे अल्जब्रेक वर्जन अफ दा अईस अलने मुडल अमने तूरेतिकली, ग्राफिकली, नुमेरिकली आईस अलनेम और अग्रिगेट दिमेंट, अग्रिगेट सप्पलाई मुडल पर बात की है, तो आज हम अल्जब्रिकल भी सहसिण है। yo' brokengg listener. тиमारकेत और बात वाया लीबार्क्येट ग़यम, जी क எन्च ती इकलिब Kons, labour market ka palade, demand curve, supply curve par bahat karenge aur pheer hum uske equilibrium par bahat karenge. So, labour market mein production function, y is the function of a, y is the total output, a for productivity, k is for capital stock, n is for labour, so y is the function of a, k and n. So, if we hold capital stock k, if we fix it, then we are using a specification of production function, in this we have fixed k, so we have dropped it. Now y is the output, it is the function of technology and labour and it is a specification of how it depends on labour. F1 and F2 are these two positive numbers. So, you know where the labour demand curve comes from? It comes from the margin product of labour. So, the requirement of firm's profit maximization is that the firm demands the same units of labour, where the product of the last unit, the margin product of labour is equal to the wage rate of the market. So, we will find the margin product of labour, it was a production function, but we have it. So, when we find the margin product of labour, you know that we will take the derivative of it with respect to n, then you will get the answer. How did we take the margin product of labour? We have derived y with respect to n. a comes from f1 n, when we take the derivative of f1, or f2 n square, sorry f2 n and 2 is not n, this is n square. So, when you take the derivative of this term with respect to n, you will get this f2 times n. So, labour demand, now what will happen? This margin product, this is the margin product. And we will equal this by the wage rate. So, this is your labour demand function. And if our labour demand. Labour supply, what is it? Labour supply, you know that the labour supply is the function of after tax real wage. W is the real wage. 1 minus T is the tax rate. So, when you multiply 1 minus T with W, this is the after tax real wage. So, this NW is positive coefficient. It is saying that when after tax real wage is added, then labour supply will be added. And N0 represents all those factors, which affect the welfare of labour supply. Working age population affects it. So, N0 captures all those factors other than the after tax real wage. So, this is the labour supply. Ok. Equilibrium. We have taken the labour demand and supply equation of the labour market. So, where will the equilibrium be? Demand and supply will be equal. And we are denoting the equilibrium level of demand and supply. So, when we solve the equation, when we solve the labour demand and supply equation of the labour market, we will put the value of Nd. Similarly, we will put the value of Ns instead of Nbar. And we will solve these two equations. So, these are the two equations. And you have two unknown variables. One is Nbar and the other one is W. Nbar is the equilibrium level of employment. And W is the real wage. So, these are the two equations. So, you know the rules of the labour market. There are two unknowns and two equations. So, you can solve them both. So, you will solve it algebraically. So, you will get these results. Ok. This is W. Real wage. And this is the employment level of Nbar. Ok. So, and when you put this Nbar in the production function, the value of Nbar is the equilibrium level of output. The F e line in ISLM model, the F e line is the value of output. So, you know the horizontal intercept. When you take F e line as R or Y, you get F e line. We will use it theoretically and numerically. We have discussed it. So, you will put the value of Nbar in this. Rest, A, F1 and F2, all these values will be given. So, it will be known. So, you will get a value of F e line. Where it will start. Ok. So, now we will see. Actually, with the help of these equations, the equilibrium value of W is the wage, the employment level is the output level. We will see how different factors will affect them. Similarly, if there is a change in productivity, it will affect the real wage, it will affect the employment level, it will affect the output. Similarly, if there is an after-tax real wage in labour supply, we have already included it. Apart from that, if we see the other factors, what will be the effect of these factors? We are taking an assumption in this. Assumption is that F1 minus F2 and not is positive. Why are we taking this assumption? To understand this assumption, I go back to that again. Basically, this numerator, we say this numerator is positive. So, it ensures that the real wage will be positive. It cannot be negative and it should be positive. So, it ensures this. Similarly, if you go back, you have a margin product. So, as a result, the margin product will also be positive. So, we can justify this without these factors. Assume that this assumption is justified. So, we will see what will be the impact of an increase in productivity. What will be the impact of equilibrium on the real wage? In an increase in productivity, the real wage will be increased. If the real wage is increased, the employment level in the labour market will be increased. N bar. And when the N bar will be increased, the full employment level of output will be increased. We can discuss all these things theoretically. But here, if you want, you can just take the derivatives. We say that the real wage will increase in equilibrium. To see this, if you go to the equation of the real wage, and take the derivative with respect to A, and you will see that the assumption we took, the sign of this derivative will be positive. Similarly, if you take the derivative with respect to A, which is familiar to the calculus in mathematics, you can do this easily. We can justify this theoretically. But numerically, you can prove it through calculus, that when you take the derivative with respect to A, the sign of this derivative will also be positive. And when N bar will increase, it means that the increase in the real wage will also increase. With respect to A, with respect to productivity, with respect to real wage, with respect to employment level, and with respect to the full employment level of output. With respect to the full employment level of output, it means that your F.E. line will shift to the right. And secondly, we want to see an increase in the N.S. N.S. means an increase in the real wage. Your working population, and other things. When that effect occurs, the value of N.N.R.T will be changed in your labor supply function. So, when your labor supply increases, then in these things, the real wage will decrease. You know that you can link it with that equation, and prove it. But the simple thing is that when the supply increases in the market, then the price will decrease. So, with respect to the labor supply, the real wage will decrease. The employment level will increase. And with respect to the employment level, the full employment level of output will also increase. And your F.E. line will shift to the right. So, today we have discussed the labor market, algebraically. So, in the next lesson, we will talk about other markets, such as goods market, and general equilibrium. Thank you very much.