Hello, I have some questions to you, just do what you can do. Thank you very much

1.

Given the demand function Qd = D(p, y0), which is a function of price p and exogenous income y0, the supply function Qs = S(p). Suppose both the D,S functions are not given in specific forms but possess continuous derivatives, if we know that supply function is strictly increasing, and demand function is strictly decreasing w.r.t price but a strictly increasing w.r.t income.

(a) Write the equilibrium condition in a single equation.

(b) Check whether the implicit-function theorem is applicable, if so find dp /dy0 , where p is the equilibrium price.

2.A monopolists average revenue function is AR(Q) = 20 30Q and his total cost function is C(Q) = 20Q2 .

Find: (1) His total revenue function (2) His profit-maximizing output level and maximum profit. (3) The price per unit at which this profit-maximizing output is sold.

3.) Suppose the value of certain cheese improves with age is given by V = 1400*(1.25)^ t . If the cost of capital under continuous compounding is 9 percent a year and there is no storage cost for aging the cheese in company caves, how long should the company store the cheese.

4.A simple economics system produces only 3 products: coal, electricity and steel. Each product is used as an input in the production of not only itself, but also the other two products as well, in such a way that: Each unit of coal requires 0.25 units of coal, 0.1 units of electricity and 0.15 units of steel. Each unit of electricity requires 0.18 units of coal, 0.2 units of electricity and 0.16 units of steel. Each unit of steel requires 0.4 units of coal, 0.3 units of electricity and 0.24 units of steel. The final consumer demands for the three products are 200 units of coal, 300 units of electricity and 400 units of steel.

(a) Write out the input-output matrix and the Leontief Matrix

(b) Find the required output levels of all three products if all demands are to be met exactly.