4. John derives utility from purchasing Blu-ray movies, B, as well as digital downloads, D. His utility function is given by

u(B, D) = log(B) + 3 log(D)

where the marginal utility of B and D are given by uB =1Band uD =3D. John has $200 to spend and the price of blu-rays, PB, is $20 and the price of digital downloads, PD, is $10.

(a) Use the marginal utilities provided above to derive John's marginal rate of substitution between the two goods.

(b) Derive John's budget constraint, derive its slope (MRT) and both of its intercepts.

(c) Use algebra and the equilibrium condition MRS = MRT to solve for John's

optimal consumption bundle.

5. Bill's Bakery is in a competitive market and faces the following cost and marginal cost

functions:

c(q) = 125 + 5q + 3q2

MC(q) = 5 + 6q

(a) Derive their profit maximizing output level as a function of market price p.

(b) Let p = 41 and find their profit maximizing output level, q?. Use q? to determine their revenue, cost, and profit for producing at this level.

(c) Based on your answer to (6b) should Bill's Bakery produce at q? or should they

shut down? Explain your answer.