7. Fred's preferences between pairs of shoes, S, and dollars available to spend on all other goods, D, can be represented by the utility function u(S, D) = SD. Because of government regulations, pairs of shoes are not sold together. Left and right shoes must be purchased separately at prices pr, and pR, respectively. Fred's endowment consists of m dollars and the price of D is 1. (a) Solve Fred's optimization problem and derive expressions for his optimal purchases and his optimized level of utility as functions of the exogenous variables (prices). (b) Fred's one-legged uncle has died and left him all his shoes (and they wear the same size.) Thus, Fred now enters the market with m dollars and Lo left shoes. Answer part (a) for this case. (Hint: Assume that Fred can sell shoes on the market for the same price that he purchases them.)

° Pizzan 4 5 2 ♡ B 4 199 0 1 2 3 4 5 6 7 8 9 10 Burgers Please refer to the graph above. A human goes to the market and must decide between buying Pizzas or Burgers for their meal. Their budget is $181. The price of a burger is $18. What is the estimated price of a pizza? about $40 O about $10 O about $30 O about $20

3. Consider a home energy storage (battery) system that can store up to 2 units of energy. At every time step, there is a demand for energy in the home which is drawn from 0,1,2 units with equal probability independent of the demands in the previous time steps. At every point in time, you have to satisfy the demand either by discharging the needed energy from the battery or purchasing power from the grid (or a combination of the two). You could also choose to purchase power from the grid to charge your battery. The grid energy price is either H(igh) or L(ow) according to a Markov chain (Price moves from H to L with probability p, and from L to H with probability q). (a) Model the decision making as an infinite horizon MDP where the objective is to minimize the discounted cost of energy purchased over an infinite horizon. (b) Write down a policy a of your choosing. Perform two steps of the operator T, for your policy, followed by one step of T..

A Define "supply." 9.( The definition of supply is very similar to that of demand. Supply is a schedule which shows the various amounts of a product sellers are at each price in a series of possible prices during a specified period, other things being equal. Supply portrays relationship between ( related either in the table or in the (graph). ) and ( ) to produce and offer for sale ) and ( ), they are (directly, inversely) S Describe and give a reason for the law of supply. The law of supply indicates that producers will produce and sell (more, less ) of their product at a high price than at a low price. This means that there is a positive, negative ) relationship between price and quantity supplied. The basic explanation is that, given product costs, a higher price means greater profits and thus more incentive for business to increase the quantity supplied.