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HW #1

Homework #1 Due in class Fri 14 Sept

This homework consists of several simple calculations using a linear demand curve and constant marginal costs. It’s the framework we’ll use all term.

Hint: When D: p = a – bQ then MR: MR = a – 2bQ. For elasticity, you should be able to do the algebra.

Base case:

    fixed costs: FC = 0
  • marginal costs: MC = c = 2
  • demand: p = D = a -bQ where a = 10, b = 1
  • marginal revenue: p = MR = a – 2bQ
  • ε (in price): ∆Q/Q / ∆p/p = ε noting that ∆p = -b∆Q and p=a-bQ
  • gross margin: (p-c)/p

1. Illustrate and/or calculate:

a.(p, Q)?


c.price elasticity of demand?

d.gross (profit) margin?

2. Let demand double for any given price. What is the new D curve? MR curve? Illustrate and/or calculate (a) – (d) as above.

3. What happens in (1) and in (2) if MC increases so that c = 4?

4. What happens in (1) and in (2) if FC = 10?


Assumptions: Saudi Arabia is 12% of global supply

OPEC is 36% of global supply

ε = 0.25 [convention leaves off the minus sign, while regression tables include]

5. What happens to global price if Saudi Arabia cuts supply by 10%? What happens to total revenues of Saudi Arabia?

6. What happens if Saudi Arabia can convince the rest of OPEC to join their supply cut?

7. At one time Saudi Arabia had marginal production costs near zero – they just had to dig a shallow hole in the ground. No longer. Does this analysis carry through if costs are $30 per barrel?

Assume the purchaser pays all transport costs. For actual prices and recent stories in the business and industry press go to: Use a round number for price that is close to reality.

8. Think and file away: What are the incentives for smaller OPEC members such as Gabon? Are they the same as for Saudi Arabia or Kuwait?  (We’re not at the point on the syllabus where we’ll discuss this.)