(a) Calculate the efficient value of Q if the total stock of the natural resource is Q = 50: Provide a graphical representation of the solution.

(b) Calculate the efficient value of Q if the total stock of the natural re source is Q = 200: Provide a graphical representation of the solution.

(c) Suppose that there is a market for the non-renewable natural resource in question. Which is the equilibrium price and quantity?

Address the following:

(a) Define the concepts of discount rate, discount factor and present value.

(b) Suppose that the allocation of a natural resource during three years results in a stream of total surplus value of $100 per period t (i.e.: t = 0, 1,2). Obtain the present value of this stream when the discount rate is r = 0:10 and also when it is r = 0.05.

(c) Alternatively, the resource could be fully extracted now (say, in the period t = 0), resulting in a total surplus $280 at t = 0 and 0 in every future period. Is this immediate extraction strategy preferred to the extraction strategy described in (a) when r = 0:10? What about when r = 0.05? What does this tell us about the intuitive meaning of discounting regarding intertemporal preferences?

(d) Explain what it means that a resource allocation is dynamically efficient.

Question 1 : Joint continuous distribution The joint PDF of random variables X and Y is given by (a) ny(:17,y) : lee5&4\") for 0 0 Determine the sample space of X and Y via a drawing and color or shade the sample space. Determine marginal PDFS. Determine the joint CDF? Make sure you specify the CDF for all XYplane. Determine cov(X, Y). If we are only interested in for the values of X Acetyl-CoA + AMP + PP, 52. The AG" for the hydrolysis of acetyl-CoA to acetate and CoA is -32.2 W/mol and that for hydrolysis of ATP to AMP and PP, is -30.5 KJ/mol. Calculate the AG" for the ATP-dependent synthesis of acetyl- CoA shown in the above equation. [R = 8.315 )/(mol K)] a. -62.7 kJ/mol b. 1.7 kJ/mol C. -1.7 kJ/mol d. 62.7 kJ/mol e. 6.3 KJ/mol 1253 Almost all cells contain the enzyme inorganic pyrophosphatase, which catalyzes the hydrolysis of PP, 10 P. What effect does the presence of this enzyme have on the synthesis of acetyl Coat Hydrolysis of pyrophosphate shifts the equilibrium of the reaction to the left, making the formation of acetyl-CoA energetically less favorable. C. Hydrolysis of pyrophosphate decreases the rate of the reaction. Hydrolysis of pyrophosphate shifts the equilibrium of the reaction to the right, making the formation of acetyl CoA energetically more favorable. Hydrolysis of pyrophosphate has no effect on the reaction e. Hydrolysis of pyrophosphate increases the rate of the reaction