ECON 212 Lecture Notes - Lecture 4: Tangent, Indifference Curve

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2 Oct 2017

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The choice is b/w saving and spending instead of two goods, there is: spending this year (c1) and spending next year (c2) The utility will be a function of the two consumption periods and within each period the consumer will earn income. Income in period will be represented i, period 1 will be i1 and income in period 2 will be i2. Example: income of ,000 this year and ,000 next year. Endowment point - point - represents the two incomes the consumer is expecting. The max consumer could spend in period 1 is (cid:2869)+ (cid:3118)(cid:2869)+ which is the c1 intercept. The max consumer could spend in period 2 is (cid:2869)(cid:4666)(cid:883)+(cid:1870)(cid:4667)+(cid:2870) which is the c2 intercept. The slope of the budget line is normally (cid:3117)(cid:3118)= (cid:4666)(cid:883)+(cid:1870)(cid:4667), therefore (cid:3117)(cid:3118)=(cid:4666)(cid:883)+(cid:1870)(cid:4667: using (cid:1868)(cid:2869)=(cid:883)+(cid:1870) and (cid:1868)(cid:2870)=(cid:883) then the budget eqn can be: (cid:2778)(cid:4666)(cid:2778)+(cid:4667)+(cid:2779)= (cid:2778)(cid:4666)(cid:2778)+(cid:4667)+(cid:2779) Put tangent into budget: (cid:883). (cid:883)(cid:2869)+(cid:886). (cid:886)(cid:2869)=(cid:887)(cid:883),(cid:882)(cid:882)(cid:882) (cid:2869) =(cid:891),(cid:884)(cid:889)(cid:884) (cid:2870) =(cid:886)(cid:882),(cid:890)(cid:882)(cid:882)

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(Exercise 3.3, Capital controls, optional) Consider a two-period model of a small open economy with a single good each period and no investment. Let preferences of the representative household be described by the utility function U(C1, C2) = â(C_1 ) + ï¢â(C_2 ) The parameter ï¢ is known as the subjective discount factor. It measures the consumerâs degree of impatience in the sense that the smaller is ï¢, the higher is the weight the consumer assigns to present consumption relative to future consumption. Assume that ï¢ = 1/1.1. The representative household has initial net foreign wealth of (1 + r0) B_0^* = 1, with r0 = 0.1, and is endowed with Q1 = 5 units of goods in period 1 and Q2 = 10 units in period 2. The world interest rate paid on assets held from period 1 to period 2, r* = 10% (i.e., r* = 0.1) and there is free international capital mobility. Calculate the equilibrium levels of consumption in period 1, C1, consumption in period 2, C2, the trade balance in period 1, TB1, and the current account balance in period 1, CA1. Suppose now that the government imposes capital controls that require that the countryâs net foreign asset position at the end of period 1 be nonnegative (B_1^* â¥ 0). Compute the equilibrium value of the domestic interest rate, r1, consumption in periods 1 and 2, and the trade and current account balances in period 1. Evaluate the effect of capital controls on welfare. Specifically, find the level of utility under capital controls and compare it to the level of utility obtained under free capital mobility. For this question and the next, suppose that the country experiences a temporary increase in the endowment of period 1 to Q1 = 9, with period 2 endowment unchanged. Calculate the effect of this output shock on C1, C2, TB1, CA1, and r1 in the case that capital is freely mobile across countries. Finally, suppose that the capital controls described in part (b) are in place. Will they still be binding (i.e., affect household behavior)?

lilacporpoise262

Consider the two-period intertemporal model that we studied in class.

(a) (5 marks) Discuss the similarities and differences between the drivers of consumption predicted by this model compared to those suggested by the traditional KeynesianconsumptionfunctionC=C(Y âT).

(b) (10 marks) Explain why this model predicts that consumption in the present and future will increase in response to either a rise in current income, or, a rise in future income. What happens to savings in each case?

(c) (15 marks) On a C1 vs. C2 diagram, sketch an indifference curve and budget constraint showing the optimal choice for a borrower. Now show the impact of an increase in the real interest rate r on the borrower, sketching two different cases: (i) where the increase in r results in a rise in period 2 consumption, and (ii) where the increase in r results in a fall in period two consumption. How can the model account for these two different cases? Discuss, what assumption must hold in each case.

Suppose, as we did in class, that consumers live for two periods and can either consume, save, or pay taxes with their income. Derive the lifetime budget constraint for the individual. What kinds of things can we say about the lifetime budget constraint? What does it imply about the consumer? Will he make his consumption choices in periods 1 and 2 independently?

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ECON 212 Lecture Notes - Lecture 4: Tangent, Indifference Curve

ECON 212 Full Course Notes

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