3. Consider a simple Robinson Crusoe model where Crusoe gets utility from consump- tion c and leisure I as u(c, 1), where u is increasing, concave and differentiable in its arguments. Crusoe faces a production function of the form y = Af(n), where n = 1-1 and A is a productivity shock. (a) Depict Crusoe's optimum graphically. Discuss the income and substitution ef- fects on n of a change in A. Do these movements create comovement between consumption and output in this model? (b) Try to provide an exhaustive list of business cycle facts. (c) What business cycle facts does this model account for?

3. Consider a simple Robinson Crusoe model where Crusoe gets utility from consump- tion c and leisure I as u(c, 1), where u is increasing, concave and differentiable in its arguments. Crusoe faces a production function of the form y = Af(n), where n = 1-1 and A is a productivity shock. (a) Depict Crusoe's optimum graphically. Discuss the income and substitution ef- fects on n of a change in A. Do these movements create comovement between consumption and output in this model? (b) Try to provide an exhaustive list of business cycle facts. (c) What business cycle facts does this model account for?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.1P

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A consumer's consumption-utility function for a two period horizon is 0.5 U(Cg,G) =C,G" he consumer's earned income stream is given by mo, m1 and the market rate of interest is r. a) Write the intertemporal budget constraint in present value terms. If the consumer does not consume anything in peripd 0, what is the most she can consume in period 1? b) Draw a graph that shows optimal consumption in each period co* and c1*. What is the slope of her budget line? c) Solve the problem for optimal consumption in each period co* and c;*. d) Suppose mọ is S50 and mị is S110 and r = 0.1. Is the consumer a borrower or a lender? Show this outcome by drawing co*. C1*, mo, mį, and bond-holdings on your graph.
3. Let Robinson Crusoe's Production Possibility curve be given by the equation: ƒ²/2 + g = 150 where f is the amount of fish and g is the amount of grain he can obtain. (think of g as plotted on the vertical axis and f as plotted on the horizontal axis). Robinson's marginal rate of substitution in consumption is MRSc = 9/f. (a) Find Robinson's production-consumption optimum R*. (b) If Robinson is discovered by a world market in which Pf = 5, and Pg = 1, determine his productive optimum Q* and consumption optimum C. (Graph the results).
Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: i. Draw the economy’s production possibility frontier on hindsight of the relevantassumption.
Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: Why are points outside the frontier unattainable?
Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: Identify three ways by which the economy can attain the level of production outside the PPF.
3. Consider the economic model of an individual's labor-leisure choice with the following components: C represents units of the consumption good L represents hours of leisure H represents hours of paid work p represents the unit price of the consumption good w represents the hourly wage rate Y represents nonlabor income T represents total time available U(C, L) represents the individual's utility function MUC denotes the marginal utility of consumption MUL denotes the marginal utility of leisure Unless otherwise instructed, assume that consumption and leisure are normal goods. Whenever graphi the model, put C on the vertical axis and L on the horizontal axis. What is the slope of the budget line? -(MUC/MUL) O-(MUL/MUC) O-W O -(w/p) O-(w+Y)/p
Assume an economy produces only two goods ( shoes and computers ) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum. Production in this economy is subjected to the laws of diminishing marginal returns and resources are assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers and vice versa is 1. On the basis of the forgoing assumptions , drawthe economy's production possibility frontier on hindsight of the relevant assumption and why the points outside the frontier unattainable?.
Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: Assume now that the sacrifice ratio is greater than 1, show what will happen to the shape of the production possibility frontier.
How do I graph this? My equilibrium I'm getting P=14 but when I plug that into the equations I'm getting Qs= 21 and Qd= 7.
2) Draw the graph of a production function which requires only one input. Suppose the decision-maker is on a budget which either can be spent on that input or on a different consumption good which can be purchased at a fixed price. Draw his possibility frontier (FF). What is the slope of the FF called and what trade-off does it refer to? Explain the condition that needs to be satisfied for him to have made a wise decision.
Assume an economy produces only two goods ( shoes and computers ) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum. Production in this economy is subjected to the laws of diminishing marginal returns and resources are assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers and vice versa is 1. On the basis of the forgoing assumptions , ( i )economy's production possibility frontier on hindsight of the relevant assumption ( ii ) why the points outside the frontier unattainable? ( III ) identify three ways by which the economy can attain the level of production outside the production possibility frontier. ( iv ) what happens to the production possibility frontier when the economy discovers an improved technology for shoes ( v ) what happens to the production possibility frontier when technological change overwhelmingly favors the production of computers. ( vi ) assume now the sacrifice…
Assume an economy produces only two goods ( shoes and computers ) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum. Production in this economy is subjected to the laws of diminishing marginal returns and resources are assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers and vice versa is 1. On the basis of the forgoing assumptions , ( i )economy's production possibility frontier on hindsight of the relevant assumption ( ii ) why the points outside the frontier unattainable? ( iv ) what happens to the production possibility frontier when the economy discovers an improved technology for shoes ( v ) what happens to the production possibility frontier when technological change overwhelmingly favors the production of computers. ( vi ) assume now the sacrifice ratio is greater than 1, show what will happen to the shape of the production possibility frontier. (vii) mention two conditions…