consumption today, c2 her consumption tomorrow, m₁ her income today, and m2 her income tomorrow. Her preferences over (C1, C2) can be represented by the utility function u(c1, c2). She can save at rate rs and borrow at rate rB. In each of the following situations, determine whether she will save, borrow, or do neither, and provide a brief explanation. 144, and rs = гB = 0.2. (a) u(c1, c2) = c1c2, m₁ = 100, m2 = (b) u(c1, c2) = ln(c₁) + 2 ln(c2), m₁ = (c) u(c1, c2)=√√c₁+0.9√√√c2, m₁ = 100, m2 = 100, m2 = 200, rs = 0.1, and rp = 0.15. 100, rs = 0.1, and rp = 0.15.

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Seung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___

Kenji is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $3.00, and a slice of pizza costs $4.00. Let E be the amount in dollars that Kenji spends on salad and pizza. If Kenji buys S bowls of salad and P slices of pizza, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation Suppose Kenji has $48.00 to spend on salad and pizza; that is, E= $48.00. Complete the following table with the values of S or P that make the equation true. Hint: To complete the first row, determine the number of pizza slices Kenji can purchase with $48.00, when the number of salad bowls he purchases is 0. Pizza Budget Salad (Dollars) (Bowls) (Slices) 48.00 0 48.00 48.00 8 0

Tim is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $4.00, and a bowl of salad costs $5.00. Let ♬ be the amount in dollars that Tim spends on pizza and salad. If Tim buys P slices of pizza and S bowls of salad, then the total amount of money he spends (B) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Tim has $40.00 to spend on pizza and salad; that is, E = $40.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Tim can purchase with $40.00, when the number of pizza slices he purchases is 0. Budget Pizza (Dollars) (Slices) 40.00 0 40.00 5 40.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Tim can purchase with a budget of $40.00. SALAD (Bowis) 14…

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..

Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)

Please explain thoroughly because I do not understand it.

Kenji is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $2.00, and a bowl of salad costs $4.00. Let E be the amount in dollars that Kenji spends on pizza and salad. If Kenji buys P slices of pizza and S bowls of salad, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Kenji has $32.00 to spend on pizza and salad; that is, E= $32.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Kenji can purchase with $32.00, when the number of pizza slices he purchases is 0. Budget Pizza Salad (Dollars) (Slices) (Bowls) 32.00 0 32.00 8 32.00 00 0