Tony Stark and Dr. Bruce Banner are trying to identify which rocket types can be switched out for others for the Endgame by calculating MRS.

Help them out by finding the partial derivatives a) ∂f/∂x and b) ∂f/∂y of

f(x,y) = (x^4) + (x^3y^2) - 2(y^3)

Wanda Maximoff and her twin, Pietro Maximoff, created a game and whoever wins will get to blow up cities in allegiance to Ultron. Assuming you are a rational consumer, how much should you expect to pay in order to play this game? The rules of the game are as follows:

Flip a coin. If it comes down heads, you get 4 dollars. If tails, flip again.

If that coin comes down heads, you get 8 dollars. If tails, flip again.

If that coin comes down heads, you get 16 dollars. Otherwise flip again and so on.

Following the changes made in the multiverse, Peter Parker is just a regular guy and is seeking employment. He's searching for a high wage from a wage distribution that is uniform on the interval (4, 7). The cost of each search is 0.03. What is the smallest wage you should accept?

Let’s suppose that your best friend Hawkeye (Clint Barton) wants you to bet on a coin flip, with the loser paying the winner £400. If your initial wealth is £650, what is the expected utility from playing this round? What is your expected utility from not playing this round? Do note that Hawkeye is risk averse

Following the destruction of other multiverses, SHIELD have noticed an excessive amount of venomous snakes. So, for every venomous snake killed, SHIELD offered a financial incentive. Eventually, however, some clever civilians began to breed cobras for the income. What type of problem is this?

Tony Stark is visiting a broker to decide where to invest his retirement funds for the next 20 years (which constitute 100\% of his savings). He visits his broker and she offers him two investments: he can invest in Project A, which is guaranteed to double his money over the 20 years, or he can invest in Project B, where there is a 50/50 chance that he will triple his money, and a 50/50 chance that he will make no gains at all and just have his original savings returned to him.

i. With a utility function $$U\left(W\right)=\ W^2$$ Robert will invest in project A

ii. With a utility function $$U=\sqrt{W}$$ Robert will invest in Project B

Thor has an investment opportunity that pays 80 with probability 1/4 and loses 40
with probability 3/4.
If his current wealth is M = 120, and his utility function is U(W) =√W Will he make
this investment?

You are tossing fair coins with Captain America. Which one of the three bets described below has the highest expected value?

Spider-Man is starting a new business. Should he self-insure against small losses?

For the avengers' function $$z=\alpha\ln x+\beta\ln y$$ which of the following combinations of expressions are correct?