Consider a closed economy with a representative consumer a

Question

Microsoft Word - ECON2152B-002_W16_Assignment3.doc

Consider a closed economy with a representative consumer, a representative firm and a government.

The representative consumer is endowed with h hours of time. Assume that the consumer has the preferences over the consumption good, c, and leisure, l, described by the following utility function.

u(c,l)= lnc + lnl.
She faces a market real wage rate, w, per hour. The consumer is assumed to have h hours

of time available, which can be allocated between leisure time, l, and time spent working

(or labour supply), denoted by N s . She receives π units of the consumption good as dividend income from the representative firm. Suppose that the government imposes a non-distortionary lump-sum tax, T, on the representative consumer. There are no distortionary income taxes.

The representative firm is a perfectly competitive firm. Assume that the representative firm produces the consumption good only with labour as an input. It has the following technology to produce the consumption good:

Y = zN d ,
where Y is the aggregate output of consumption goods produced by the firm, z is the

exogenous total factor productivity and N d is the hours of labour employed by the firm. The firm faces a market real wage rate, w, per hour.

The government purchases exogenously fixed G units of consumption goods from the firm. Assume that G is always positive. It fully finances this purchase with lump-sum taxes collected from the consumer. That is, the government purchases are equal to lump- sum taxes, in real terms.Page 1 of 2 Pages

1. a)  Define a competitive equilibrium for this economy. [2.5 marks]
2. b)  Determine the Pareto-optimal levels of employment, consumption and output. Illustrate your results on a diagram. [Notes/Hints: Show all steps of your calculations to get full marks. Express the equilibrium levels of all endogenous variables in terms only exogenous variables. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.] 
3. c)  State the second fundamental theorem of welfare economics. Briefly explain why this theorem holds for this economy. Apply this theorem to determine the competitive equilibrium wage rate, and the competitive equilibrium levels of employment, consumption, output, and lump-sum tax. Illustrate your results on the diagram which you drew in part (b). [Notes/Hints: Show all steps of your calculations to get full marks. Express the equilibrium levels of all endogenous variables in terms only exogenous variables. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.] 
4. d)  Suppose that there is an increase in government purchases, G. Determine mathematically the effects of this increase in G on consumption, output, employment, and wage rate in the competitive equilibrium. Provide an intuition for each of these effects. Illustrate the effects of this increase in G on a separate diagram. [Notes/Hints: Show all steps of your calculations to get full marks. You have to take a partial derivative of the endogenous variables with respect to G and determine whether the result is positive or negative. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.] 
5. e)  Are the predictions of the model economy about the effects of an increase in G on the equilibrium levels of consumption, output, employment and wage rate consistent with the business cycle facts? Explain.