PROBLEM (1) (Rational Choice) Suppose your friend is about to buy a digital camera. A digital camera is identified with three dimensions; 1) resolution (in megapixels), 2) optical zoom (a real number) and 3) battery life (a number of hours). For example, A = (8, 4, 20) is a camera with 8mp resolution and x4 optical zoom and 20 hours of battery life. When he goes into a store, he faces a menu of cameras. When comparing two cameras if camera A is weakly better than B on at least 2 dimensions, it is weakly preferred to the other; written A ≥preferred B. a) Is this preference relation complete? Transitive? Prove it or show an example where the property doesn't hold. b) Suppose the agent chooses from any menu of cameras, a camera that is (weakly) preferred to all other cameras in the menu. Would this choice function be rational, given (a)? Briefly explain your reasoning.

(3 points) When sold for $259,000.00, Ferraris have an annual supply of 6758 vehicles and an annual demand of 6691 vehicles. When their price increases to $279,000.00, the annual supply increases to 6913, and the demand decreases to 6010 billion gallons. (a) Assuming that the supply and demand equations are linear, Afind the supply and demand equations. Supply Equation p = Demand Equationp (Note: The equations should be in the form p = mg + b where p denotes the price (in dollars) and q denotes the quantity. The slope and y-intercept should be accurate to two decimal places). (b) Find the Equilibrium price and quantity. Equilibrium price p = Equilibrium quantity q = (Note: The equilibrium price and quantity should be accurate to two decimal places, and the equilibrium price should include a dollar sign).

Jack and Diane work at a bakery. Jack can make either five batches of cookies or two cakes per hour, while Diane can make either four batches of cookies or three cakes per hour. At 9:00 a.m. they receive an order for 24 batches of cookies and nine cakes. What time is the soonest they can have the order ready?

Q.3 - An economist has estimated demand of D = 1000 − P and Supply of S = 400 + 10R for onions, where R is the number of days of rainfall. (a) Plot the demand and supply curves. (b) Show the equilibrium quantity and the equilibrium price on the graph. (c) Use Algebra to determine the equilibrium price and quantity (d) Use a new graph of demand and supply curves to show the effect of an increase in rainfall