5. (15%) A consumer has $100 to divide between purchasing wine and quiche. Suppose wine costs $10per bottle if the consumer purchases up to 5 bottles. After that, it is $5 per bottle. Supposequiche is $5 each. Please draw the budget line. Will a consumer purchase exact 5 bottles of wine?And why? (Explain it using both the graph and words)

6. (15%) A firm can manufacture a product according to the production function Q = 2(K)^1/2 (L)^1/2 where K represents capital equipment and L is labor. The company has already spent $10,000 on the 4 units capital.

a. Please show the expression for the average product of labor, APL and the marginal product oflabor, MPL.

b. If workers at the firm are paid a competitive wage of $100 and the product is sold for $200 each, what is optimal level of labor usage and what is the maximum profit?

7. (15%) A multiproduct firm's cost function is C(Q ,Q ) = 50 + 0.2Q₁² + 0.1Q₂²

a. Are there economies of scope? Why?

b. Are there cost complementarities in producing products 1 and 2? Why?