1. Consider the following utility for Allison who consumes goods T and good Z: U (T, Z) = T0.1 Z0.9. Allison has an income I = 500 that she totally uses to purchase goods T and Z at the respective prices PT= 2 and PZ= 3.
a- Set up the budget constraint for Allison
b- Derive Allison's demands for goods T and Z
c- Calculate the marginal rate of substitution of T for Z.
2. Consider the following production function for a firm that uses only one input (labor) and produces one output V. F (l) = V = 100 l1/2.
a- Derive the firm's output supply and labor demand functions
b- How much labor will the firm hire and how much of the good V will it produce if the selling price of good V is PV = 1 and the wage rate w = 20?
c- Compute the profit under the conditions in question b.
3. Consider the following production function for a firm that uses only one input (labor) and produces one output N. F (l) = N = 75 l1/3.
d- Derive the firm's output supply and labor demand functions
e- How much labor will the firm hire and how much of the good V will it produce if the selling price of good V is PN = 2 and the wage rate w = 20?
f- Compute the profit under these conditions
4. Consider the following firm with the production function Q = F (L) = 2 L1/2. L = Labor. Wage w= 12. Fixed costs is FC = 500 (Sunk cost). Derive the short run cost function. Graph this function using excel.
5. Consider the following company that has two firms (plants) for producing a good X. firm A has a cost function CA = 650 QA - 2 (QA2) and firm B cost is CB = 600 QB - 3 (QB2).The firm wants to produce a total of 100 units of good X. or QA+ QB =100. Find the least costly way of production for this company