Group-Assignment for Part-I: work out questions; 1) Given utility function U = X0.5y0.5, where Px = 12 Birr, Py = 4 Birr and the income of the consumer is M = 240 Birr, then; a) Find the utility maximizing combination of X and Y b) Calculate the marginal rate of substitution of X for Y (MRSxy) at equilibrium and interpret the result. 2) Assume a budget line is drawn for two commodities: X on the x-axis and Y on the y-axis. If the income of the consumer is 120 Birr, the y-intercept is 3, and the slope of the budget line is -0.5 then determined the price of commodity X. 3) Given market demand: Qa = 100 -0.75P, and market supply: P = 40, +80, where Q is quantity demand, Q, is the quantity supply, and P is the price of the commodity A) Calculate the market equilibrium price and quantity B) Determine, whether there is surplus or shortage at P 100, and P-120 C) The price elasticity of demand at equilibrium and interpret your result 4) Suppose a firm operates in a perfectly competitive market. The market price of its product is 4 birr and the total cost function is given by, TC = -5Q² +200 + 50, Where; TC is the total cost and Qis the level of output. A) What level of output should the firm produce to maximize its profit B) Determine the level of profit at equilibrium C) What minimum price is required by the firm to stay in the market and determine the shutdown point level of output? D) Find the minimum value of average variable cost (AVC) and marginal cost (MC)​