## Are consumers better off or worse off as a result of the demand increase?

The Ministry of Tourism in the Republic of Palau estimates that the demand for its scuba diving tours is given by Q^D = 6,000 – 20P, where Q is the number of divers served each month and P is the price of a two-tank dive. The supply of scuba diving tours is given by Q^S = 30P – 2,000. a. Solve for the equilibrium price and quantity. b. Find the value of the consumer surplus received by divers visiting Palau. (Hint: It may help to draw a graph.) c. Find the value of producer surplus received by dive shops. (Hint: It may help to draw a graph.) d. Suppose that the demand for scuba diving services increases, and that the new demand is given by Q^D = 7,000 – 20P. Calculate the impact of this change in demand on the values you calculated in parts (a) through (c). e. Are consumers better off or worse off as a result of the demand increase? How about producers?

### Prove that the hypothesis class of all conjunctions over d variables is PAC learnable and bound its sample complexity.

1.  In this question, we study the hypothesis class of Boolean conjunctions defined as follows. The instance space is X ={0,1}d and the label set is Y ={0,1}. A literal over the variables x1, . . ., xd is a….

### Show that for every probability distribution D, the Bayes optimal predictor fD is optimal, in the sense that for every classifier g from X to {0,1}, LD( fD) ≤ LD(g).

1. Let H be a hypothesis class of binary classifiers. Show that if H is agnostic PAC learnable, then His PAC learnable as well. Furthermore, if A is a successful agnostic PAC learner for H, then A is also a….

### . Show that the algorithm just described satisfies the requirements for being a RP solver for ERMH.

1. On the basis of the preceding, prove that for any k ≥ 3, the ERMHnk problem is NP-hard. 2 In this exercise we show that hardness of solving the ERM problem is equivalent….