Kindly. solve the following questions.

Problem 1: motivating workforce (7 Pts.) An individual has preferences over leisure hours during the day (21 ) and dollars spent on consumption of goods (12) given by u(71, 12) = 1412 Her endowment is (24,0), and her hourly wage is $ 10. a) Find the individual's choice of leisure and consumption (r;, r;), and her supply of labor s" b) Her employer, who needs to motivate her to work some more hours, is contemplating two possible solutions: either raise the salary to $14, or pay her overtime: keep the salary to $10 for the first s' hours of work (the s' you found in item a)), but raise it to $16 for any hour worked above s'. Find the individual's supply of labor under the two schemes to figure out which of the two approaches is more succesful. (Hint: for overtime, draw carefully the budget set, and the indifference curve going through the choice (ar;. r;) from a), to understand what is going on). c) Even if you had not found the exact labor supplies in part b), could you make a general argument, independent of the particular utility and the wages at play, for why one of the two payment schemes would be more succsessful than the other?Consider a market where technology is characterized by a constant average and marginal cost given of $10 to the firm. The market demand curve is given by 0 =45 - 1/2 P a) Compute the total surplus under perfect competition. b) If the market is characterized by a uniform pricing monopolist, compute the deadweight loss that results when the monopolist charges the profit maximizing price. 0) If, instead, the monopolist also used an entry fee, what combination of price (per unit) and entry fee should the monopolist use to maximize profit? d) If instead, the market is characterized as a duopoiy with two identical firms selling identical products and setting prices in a simultaneous move, static game, compute the Nash equilibrium prices for the firms to charge. 3) If there are five consumers with demands identical to the market demand curve given in the original question stem, find an expression for the total willingness to pay for the society of five consumer segments as a function of the total quantity demanded in the market if the good is non-rival and non-excludable. 5) In this question, we're going to use a game tree and backward induction to analyze a Stackelberg problem. In this case, each firm has 3 options: to produce a low level of output, a medium level of output, or a high level of output. The payoffs to each firm given each firm's output choice are: (KA, KB) B: High B:Medium B: Low A: High (0,0) (75,50) (112.50, 56.25) A: Medium (50,75) (100, 100) (125, 93.75) A: Low (56.25, 112.50) (93.75, 125) (112.50, 112.50) a) What is the Nash equilibrium when both firms choose their output at the same time? Explain. You must prove that your answer satisfies the definition of Nash equilibrium. b) Now assume that firm A can choose its output first. Fill in the following game tree for this sequential game. Each of the 9 payoff combinations above corresponds to one of the 9 endpoints of the game tree. I've filled in (Med, High) to get you started. A chooses L M H B chooses L M H M H M H A M. B-H (50,75) c) Now that you've filled in the tree, use backward induction to find the equilibrium for this game. Briefly describe why your answer is different than in 6a. Figure out B's best response to each of A's possible actions. Then, pick the one of those three options that maximizes A's profit, given how B will respond.(a) A "unit step" signal u(t) (i.e., a unit-step waveform) is defined by the equation u(t) = 0 for t 0, by x(a, t) = 0 for t