Note: There could be several questions on this economy. Answer each one carefully and record your answer taking into account that your answer may be relevant to the question(s) that may follow. Consider a 'production economy' with two goods, X and Y, and two inputs, L (labour) and K (capital) such the the production function of each good is given by X=F(Lx,Kx)=axLxbxK(1bx)Y=G(Ly,Ky)=ay,LybKy(1by) where Lj and Kj denote respectively the amount of labour and capital used in the production of good J, J=X, Y. Assume that ax=ay=1,bx=1/2 and by=1/2. Furthermore, suppose that the aggregate demand for good X and the aggregate demand for good Y are given respectively by Demand for X:xPaM Demand for Y:yPy(1a)M where pJ denotes the price of good J,J=X,Y, M denotes "national income", and the preference/demand parameter is a=0.8 Finally, assume that the economy has 243 units of labour and 195 units of capital. Let w denote the price of labour and r denote the price of capital. What is the equilibrium value of the price of capital, r, if the equilibrium price of labour is w=1 ? Note: There could be several questions on this economy. Answer each one carefully and record your answer taking into account that your answer may be relevant to the question(s) that may follow. Consider a 'production economy' with two goods, X and Y, and two inputs, L (labour) and K (capital) such the the production function of each good is given by X=F(Lx,Kx)=axLxbxK(1bx)Y=G(Ly,Ky)=ay,LybKy(1by) where Lj and Kj denote respectively the amount of labour and capital used in the production of good J, J=X, Y. Assume that ax=ay=1,bx=1/2 and by=1/2. Furthermore, suppose that the aggregate demand for good X and the aggregate demand for good Y are given respectively by Demand for X:xPaM Demand for Y:yPy(1a)M where pJ denotes the price of good J,J=X,Y, M denotes "national income", and the preference/demand parameter is a=0.8 Finally, assume that the economy has 243 units of labour and 195 units of capital. Let w denote the price of labour and r denote the price of capital. What is the equilibrium value of the price of capital, r, if the equilibrium price of labour is w=1