Natural gas is a depleteable resource. Suppose that society has two time periods (t=0 and t=1). If the demand for natural gas is given by: Qpt= 24-4Pt. The marginal extraction cost is $2. What is the least amount of natural gas reserves that would avoid having intertemporal scarcity?
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- Q25. Given demand and supply for the Cobweb model as follows, find the intertemporal equilibrium price, and determine whether the equilibrium is stable; (i) Qdt = 18-3P Ost = -3 +4Pt-1 (ii) Qdt = 22-3P Qst = -2 + Pt-1Q4 (i) A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6t2 + 5t (t + 1)2. What happens to production in the long run ? (ii) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x) /x3 + x2 + 4x.Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?Consider the one-sector Schumpeterian model in discrete time analyzed in the previous exercise, except that now (.) denotes the probability of innovation, and each innovation improves the quality of a machine q to λq, where λ > 1. Suppose that when a new innovation arrives a fraction ϕ of workers employed in the final good production are unable to adapt to this new technology and need to remain unemployed for one time period to “retool.” (a) Define the equilibrium and steady-state (BGP) allocations. [Hint: also specify the number of unemployed workers in equilibrium.] (b) Define the appropriate generalization of the steady state for this economy, and determine the number of unemployed workers in this equilibrium. (c) Show that the economy experiences bursts of unemployment followed by periods of full employment. (d) Show that a decline in ρ increases the average growth rate and the average unemployment rate in the economy.
- Suppose the market demand curve for a non-renewable resource is given by: Q=2000-40P. Consider a finite-period model. Which of the following are true? Suppose the marginal cost of extraction is constantly at 40. Suppose the risk-free interest rate is 10% Select all correct answers. a. When there is plenty of this resource, the marginal user cost can be zero in all periods on the optimal extraction path. b. If marginal user cost is 2 in a given period on the optimal path, the marginal user cost should be 2.2 in the previous period c. The dynamically efficient extraction quantity is 400 per period until the resource is exhausted. d. When 200 units are exhausted in a given period, the marginal user cost is 5.__________ refers to any situation in which disequilibrium is caused by one aspect of a society failing to change atthe same rate as an interrelated aspecConsider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. The constant social marginal cost of extraction is 40 in each period and the total stock of the resource is Q = 300 units. Moreover, the social marginal beneÖt is MB(Qt) = 200 Qt, where Qt is the quantity of resource extracted in period t, for t = 0; 1. The discount factor is 0:8.(a) What is the efficient quantity of resources extracted in each period? Provide a graphical representation of the solution. (b) What is the marginal user cost (or scarcity rent) of the resource in each period? (c) Suppose that there is a market to trade the resource. What is the equilibrium price corresponding to each period? Justify the answer. (d) Suppose that it is now expected that because of an extraction technol- ogy improvement, while the Örst period marginal cost of extraction will still remain MXC1 = 40, the second period one will now de- crease to MXC2 = 20. Answer the previous…
- Consider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. The constant social marginal cost of extraction is 40 in each period and the total stock of the resource is Q = 300 units. Moreover, the social marginal beneÖt is MB(Qt) = 200 Qt, where Qt is the quantity of resource extracted in period t, for t = 0; 1. The discount factor is 0:8.(a) What is the efficient quantity of resources extracted in each period? Provide a graphical representation of the solution. (b) What is the marginal user cost (or scarcity rent) of the resource in each period?A theoretical model attempts to identify every possible determinant of an event. True FalseThe unemployment rate in the U.S during during the Covid-19 pandemic is estimated to have reached about A 9.9% B. 16.1% C. 13.3% D. 8.8% E. 20.0%
- “The oil Price run-up of 2007-08 was caused by strong demand confronting stagnating world production. Although the causes were different, the consequences for the economy appear to have been very similar to those observed in earlier episodes, with significant effects on overall consumption spending and purchases of domestic automobiles in particular. The experience of 2007-08 should thus be added to the list of recessions to which oil prices appear to have made a material contribution.” Source: Hamilton, J.D., 2009. Causes and Consequences of the Oil Shock of 2007-08 (No. w15002). National Bureau of Economic Research. a) Oil price shocks have an evident impact on the short run aggregate supply curve. With the help of a graph demonstrate how rising oil prices affect the SRAS and explain what other factors can cause this shift. b) Different theories…Compare two versions of the two-period depletable resource model that differ only in the treatment of marginal extraction cost. Assume that in the second version the constant marginal extraction cost is lower in the second period than the first (perhaps due to the anticipated arrival of a new, superior extraction technology). The constant marginal extraction cost is the same in both periods in the first version and is equal to the marginal extraction cost in the first period of the second version. In a dynamic efficient allocation, how would the extraction profile in the second version differ from the first? Would relatively more or less be allocated to the second period in the second version than in the first version? Would the marginal user cost be higher or lower in the second version? Why?CThe following Mundell-Fleming model of a small, open economy will be used in all numerical exercises. It assumes a short-run framework in which prices are constant and output is demand-determined. C=200+0.8(Y-T) I=500-30r NX=10-100e M/P=50+Y-60r r=2 G=200 T=100 M=4000 P=2 The above values of exogenous variables will be referred to as their original values in the questions below. For this question, assume that the exchange rate is floating. (a) Derive the equilibrium equations for IS* and LM* , sketch a graph of the two equations and solve for the equilibrium values of Y, e and NX.