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Suppose we are planning power system operations for 4 hours. Demand in the four hours is 350, 480, 460, and 380 MW, respectively. We have a collection of zero-cost variable resources with output of 0, 80, 40, and 0 MW in the four hours. We also have a collection of thermal assets with a cost function f(x) = .05x 2 (e.g., it costs $500 to produce 100 MW for an hour and $2000 to produce 200 MW for an hour). As in Problem 2, we can also curtail load at a cost of $10,000/MWh. Construct a model in Excel describing this system and solve to determine an optimal production schedule for the three resources (variable, thermal, and demand). Since the problem is nonlinear, you will need to choose the GRG Nonlinear solving method rather than Simplex LP.

Suppose that there are three states of the world, a, b, and c. The probabilities of the three states are 1 = 0.25, 2 = 0.5, and 3 = 0.25. Let A, B, and C denote the Arrow-Debreu securities that pay $1 in states a, b, and c, respectively. That is, A = (1,0,0), B = (0,1,0) and C = (0,0,1). Let pA = 0.4, pB = 0.5 and pC = 0.2 denote the prices of A, B, and C.

Consider a security X which is worth $2 in state a, $3 in state b, and $1 in state c. If there are liquid markets for A, B, C and X, what is the price of X?

Production functions, inputs are perfect complements) Fine epoxy is used to produce LEDs and other electrical components. To get stable, good qualities (durability, resistance, adhesion) epoxy, the epoxy resins (R) are cured ("linked") to hardeners (H) like amines and acids, at the following fixed proportion: to produce 1 unit of final epoxy, we need to cure 2 units of R with 1 unit of H. Let be the quantity of final epoxy produced, (, ).

Then, the production function of epoxy is given by: (, ) = 1 2 min(, ), for some positive numbers and .

a. What is and ?

b. If we want to produce 10 units of the final product epoxy, what would be the least amount needed of R and H?

c. Does the production function of epoxy exhibit increasing, constant, or decreasing returns to scale? (IRS, CRS, or DRS?)

d. Draw a map of some isoquants of this production function

Suppose that there are three states of the world, a, b, and c. The probabilities of the three states are 1 = 0.25, 2 = 0.5, and 3 = 0.25. Let A, B, and C denote the Arrow-Debreu securities that pay $1 in states a, b, and c, respectively. That is, A = (1,0,0), B = (0,1,0) and C = (0,0,1). Let pA = 0.4, pB = 0.5 and pC = 0.2 denote the prices of A, B, and C.

Consider a security X which is worth $2 in state a, $3 in state b, and $1 in state c. If there are liquid markets for A, B, C and X, what is the price of X