①A’s endowment is composed of 30 unites of good 1 and40 unites of good 2. and the price of good 1 and good 2 are p1 and p2.A has no income and her unility function is U(x1, x2)=(X1-3)(X2-4)

1.    what is A’s budget constraint.

2.    write out the Lagrangian function for theutility-maximization problem.

3.    find her ordinary demand function?

②G’s income is 200 per month, and her utility functionis U(x1,x2)=x12(x2)3

1. write out the Lagrangian function.

2. Find her ordinary demand function.

3. Is good 1 normal or inferior? Is good 2 normal orinferior?

4. what is the price elasticity of demand for good 1and good 2?

③Consider the following utility function:U(x1, x2)=5x2+15x1-(x1)2/6

1. find the ordinary demand function for good 1. Isquantity demanded dependent on income?

2. Find the compensated demand function for good 1.

3. Comnpare the two demand functions, and explain theresult in terms of the absence of income effect on the demand for good 1.

④A firm owns two plants that produce the same good. Themarginal cost function for the two plants are : SMC1=3y1    SMC2=7y2

Where y1 and y2 are quantitiesof output produced in each plant.

1.    if the firm wants to produce 20 unites ofoutput at minimum cost, how much should it produce in each plant?

2.    Now consider an arbitrary quantity ofoutput y. To minimize costs, what function of the total output should the firmproduce in each plant?

⑤A perfectly competitive market has demand curveP=18-0.05Y. If every firm in the industry has an average cost functionAC=9/y+y.

1. what is the equilibrium price and qunatity in themarket?

2. What is the long-run equilibrium number if firms?

3. find the market supply function

4. calculate the producer and consumer surplus forthis competitive equilibrium.