Consider the following exchange economy: u (x1, x2) = min{2x1, x2} u³ (x, x2) = min{x, 2x} = (2, 2) B = (2, 2) Let P₁/p2 denote the relative price. Suppose = 1. = (a) Show that both markets clear at this relative price by computing the optimal consumption plan for each consumer and showing that these plans are feasible. [25 marks] (b) What is the associated WEA? How many units are bought and sold on each market? [10 marks] (c) Illustrate this equilibrium in an Edgeworth Box diagram. Your diagram should include the WEA, the budget line, and each con- sumer's indifference curve through the WEA. [15 marks]

Could you use formulas in order to get those answers, like the images I have attached to this follow-up questions?

Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R = 250: –$200, –$100, $0, $100, $200, $300, $400, $500.

Derive the Karush-Kuhn-Tucker conditions for this Bid-price policy program (also shown in the image for clarity),min J˜µT(x)s.t. µ ≥ 0with variable µ ∈ ℝ^m. In particular, show that an optimal solution µ* to this program must satisfy the constraints in the image below:

Explain in detail how you would extend the Cox-Ross-Rubinstein binomial tree model for pricing options if instead of considering two states of nature in each period you consider three states of nature (e.g. a good state, a middle state and a bad state). Focus on a tree with two periods (periods 0, 1 and 2) and draw the corresponging trinomial tree

Construct the payoff piecewise function from a bull spread when puts with strike prices K1 and K2, with K2 > K1, are used.

12) Suppose that demand is given by the equation: P = 10 - 0.2QD and supply is given by the equation: P = 2 + 0.2Qs. Find the equilibrium price and quantity.

5. (Replicating strategy for pricing) To price a derivative, we can use risk-neutral pricing. As an alternative yet equivalent method, we can construct price the derivative using replicating strategies. Consider a 1-period binomial model, where we have three nodes No.0, N1.0, N1.1. We have a cash account with fixed interest rate r = 0.01 - that is, if we have at No.0 cash account with D dollars, we expect (1+ r)D at either N1.0 or N1.1. We also have a stock with price S0.0 10 at No,0, S1,0 = 8 at N1,0 and S1,1 = 15 at N1,1. Now consider an European call option at time t = 1 with strike K = 12. Can you price the option at No.0 using a replicating strategy, and what is the price? Please submit your answer rounded to only one decimal digit - for example if your answer is 1.28, then submit 1.3. If your answer is 1.12, submit 1.1.

please answer the question attached in the image below

On a graph for a representative firm in a perfectly competitive industry, depict the three cost curves AVC, ATC, and MC (assume typical U-shaped cost curves). Now assume the market price, P, is such that it intersects the upward-sloping portion of MC above ATC. Graphically depict the short-run equilibrium q (representative firm's output) and π (representative firm's profit) under this price scenario Given the situation you graphically depicted in Question 4, please state the level of economic profits (positive, zero, negative) of this representative firm and explain why this is the case.