please answer the question a and b

Question 1. (20 marks) a. Consider the national income model with the following equations. Y =C+I+Go I = f (u,r) C = 6Co where Y is income, I is investment, C is consumption, Go is government expenditure, H measures the level of investor confidence, and r is the interest rate. f is a non-linear function. i ) Using differentials, find - and -.(8 marks) ii) Suggest (economically meaningful) conditions on the functions f so that - is I du positive and - is negative. (4 marks) iii) Using a diagram with Y on the horizontal axis and aggregate expenditure on the vertical axis, depict how an exogenous change in u and r affect the equilibrium level of income Y. (3 marks) b. Consider a monopolist with no production costs who produces two goods: good X and good Y. The inverse demand function for good X is Px = 3 - x and the inverse demand function for good Y is Py = 6 - y. Find the optimal levels of x and y