Please solve the following questions

Consider an economy described by the following equations: Aggregate consumption: C : 400 + 0.2(Y T ); Aggregate investment: I = 120 10f ; Government sector: G = T = 100. o Derive the aggregate demand function; 0 Calculate the equilibrium level of income. 0 What is the effect of an increase in the interest rate on the equilibrilnn level of income? The following production function describes the output of a local Pittsburgh mime troupe's performances given the labor of its performers: q = 217 where q denotes the hours of performances provided and I denotes hours of labor input by performers. The troupe is a price-taker both for performances (which sell for P) and for performers (which can be hired at the wage rate of w per hour). What is the total cost function [C (q)] for the troupe? b. Solve for the profit maximizing number of performer hours [(P, w)], i.e., the troupe's demand for labor. What is the profit function [x(P, w)] for this troupe? Describe the homogeneity of the profit function with respect to P and w. C. What is the supply function [q(P, w)] for the troupe's mime performances? d Use the envelope theorem (Shephard's Lemma) and the profit function you found in part (b) to double check your derivation of the troupe's demand for labor function [1(P, w)].Consider the following function: f(x1, X2) = Ax1.5+x2 where x, 2 0, X2 2 0, A 2 0, 0 0 and faces prices p, and p2 respectively for goods x1 and X2. i) Derive and describe the demand of the consumer for goods x, and x2. [20 marks]